# Math Is Fun Forum

Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

You are not logged in.

## #1 Help Me ! » Exponential and Logarithm functions » 2022-09-27 00:53:07

Replies: 4

Hello,

I can't solve this exercise.

In an earthquake, a Seismic wave travels through the Earth layer, which gives out an energy that causes the earth to shake and also gives out low frequency acoustic energy.  The instrument seismograph is based on a logarithmic scale, called the Richter Scale.  Since it’s a base 10 scale each number increase on the scale indicates an intensity 10 times stronger than the previous number on the scale.

The Midlands of South Carolina have been experiencing a “swarm” of earthquakes in recent months.  The strongest registered 3.7 on the Richter Scale.  If the smallest recorded during the swarm was 2.7, what is the mathematical relationship between the two recorded earthquakes?  Explain.

Thank you,

## #2 Re: Help Me ! » Range and domain of functions » 2022-09-07 09:57:51

Hello,

I have completed these exercises about finding the domain and range. Are they correct?

3. y = 20 - 2x^2

Domain: (-∞, +∞)
Range: (-∞, 20)

4. y = 25(-7x-4)^64

Domain: (-∞, ∞)
Range: (0,  ∞)

Thank you so much,

## #3 Help Me ! » Range and domain of functions » 2022-09-06 09:39:32

Replies: 6

Hello,

I can't solve this exercise.

What is the domain and range of the function:

y = x^2 / (x^2-16)

Thank you so much,

## #4 Help Me ! » Direct, Inverse, and Joint Variations » 2022-09-04 02:59:02

Replies: 1

Hello,

I need help with these two exercises.

3   If y varies directly as x and z and y is 5 when x is 3 and z is 4, find y when x is 2 and z is 3.  Show steps,

Direct => y = kx

5 = k*3

5/3 = (k*3)/3

k = 5/3

y = (5/3)x

y = (5/3)*2

y = 10/3 = 3.333...

Direct => y = kz

5 = k4

5/4 = (k*4)/4

k = 5/4

y = (5/4)z

y = (5/4)*3

y = 15/4 = 3.75    (HOW DO I NOT LOSE Z?)

9      If w varies directly with f and inversely with g and w = 5 when f = 2 and g = 7, find w when f = 4 and g = 9.

Direct => w = kf

5 = 2k

k = 5/2 = 2.5

w = 2.5 * 4

w = 10

Inverse => w = k/g

5 = k/7

k = 7*5 = 35

w = 35/9 = 3.888...9   (HOW DO I NOT LOSE G?)

Thank you so much,

## #5 Re: Help Me ! » Inverse Functions » 2022-08-30 05:35:34

Hello,

Does this look correct considering the feedback in the parenthesis?
10. Dwight will be celebrating his 7th birthday with a swimming party that his parents are planning for him.  The facility rents for \$500 plus \$25 per guest including lunch and drinks.  How many guests can they invite if their budget is \$2500?

(Show the equation substituting into y and then how to solve the equation for x)

y = mx + b

y = 25x + 500

2500 = 25x + 500

25x = 2000

x = 80 guests

## #6 Re: Help Me ! » Inverse Functions » 2022-08-22 04:15:50

Hello,

I have one last exercise I need to check if it is correct.

Dwight will be celebrating his 7th birthday with a swimming party that his parents are planning for him.  The facility rents for \$500 plus \$25 per guest including lunch and drinks.  How many guests can they invite if their budget is \$2500?

2500 - 500 = 2000
2000/25 = 80 guests

## #7 Re: Help Me ! » Inverse Functions » 2022-08-14 02:22:29

Hello,

Thank you so much for your detailed explanation!

This is what I came up with f(g(x)) for exercise 8.

f(g(x))= f (-5x + 3) = -1/5 (-5x + 3) + 3/5 =
(After that I am stuck and don't know how to get x as the result.)

This is the result for f(g(x)) for exercise 9.

f(g(x))= f (x -1/2) = x - 1/2 + 1/2 = x - 0 = x
(IS THIS CORRECT?)

## #8 Re: Help Me ! » Inverse Functions » 2022-08-13 09:59:42

Hello,

Thank you for your help! This is what the teacher is telling me about how to do these exercises.

Step 1  Find f(g(x)).

Step 2  Find g(f(x)).

Step 3  If both Step 1 and Step 3 have x as the result, then they are inverses.

The problem is that I can't solve the first two steps for exercises 8 and 9.

## #9 Help Me ! » Inverse Functions » 2022-08-10 10:51:01

Replies: 11

Hello,

I can't solve these two exercises.

C   Are f and g inverses of each other?  Support your response algebraically.

8   f(x) = -(⅕)x + (⅗), g(x) = -5x + 3

9   f(x) = x + ½, g(x) = x - ½

Thank you so much,

## #10 Help Me ! » Domain of a Composite Function » 2022-08-02 11:12:04

Replies: 1

Hello,

I can't figure out what the domain for this exercise is for days. Can someone help me?

7   f(x) = 2x + 3 and g(x) = –x^2 + 5, find (g o g) (x).

(g o g) (x) = g (g(x))

= g (-x^2 + 5)

= (- (-x^2 + 5) ^2 + 5)

= (-(-x^2 + 5) (-x^2 + 5) + 5)

= (- (x^4 -10x^2 + 25) + 5)

= -x^4 + 10x^2 - 20

Thank you,

## #11 Help Me ! » Composition of Functions » 2022-07-24 19:10:25

Replies: 2

Hello,

Can I get feedback on if these look correct?

1    Given f = { (-1, 8), (3, -1), (-2, 0) } and g =  { (-5, 8), (3, -1), (-1, 0) } .  Find (f o g)(3).  Show steps,

( f o g)(3) = f ( g(3) ) = f(-1) = 3   (IS THIS CORRECT?)

2   Given f = { (-1, 8), (3, -1), (-2, 0) } and g =  { (-5, 8), (3, -1), (-1, 0) } .  Find (g o f)(3). Show steps,

( g o f)(3) = g ( f(3) ) = g(-1) = 3   (IS THIS CORRECT?)

5   f(x) = 15x -12 and g(x) = -15x^2 + 14x - 10, find (f o g)(-1).

( f o g)(-1) = f ( g(-1) )

g(-1) = -15^2 + 14(-1) - 10 = -249

f(-249) = 15(-249) - 12 = -3747

(f o g)(-1) = -3747   (FOR THIS ONE I WAS TOLD THAT -15 IS NOT SQUARED, BUT IN THE G FUNCTION IT IS SQUARED. WHAT AM I SUPPOSED TO CHANGE?)

Is it supposed to be done like this:

(f o g)(-1) = f( g(x))
f( -15^2 + 14x - 10)
15x ( -15^2 + 14x - 10) - 12
-3375x + 210x^2 -150x - 12
= 210^2 -3525x - 12

6    f(x) = -13x2 -13x + 14 and g(x) = -13x - 11, find (g(g(-3)).
(g o g)(-3) = g ( g(-3))

= g ( (-13x - 11) )

= -13 (-13x - 11) -11

= -169x + 143 - 11

= 169x + 132    (THE FEEDBACK WAS THAT FIRST, g(-3)) PUT -3 IN THE G FUNCTION AND THEN SIMPLIFY)

Is it supposed to go like this:

(g o g)(-3) = g ( g(-3))

g(-3) = -13(-3) -11 = 28

(g o g)(-3) = 28

7   f(x) = 2x + 3 and g(x) = –x^2 + 5, find (g o g)(x).

(g o g)(x) = g (g(x))

= g (-x^2 + 5)

= √(-x^2 + 5)

= -x + 5   Domain: {x:x Ð„ R}   (I WAS TOLD THAT THE RADICAL SHOULDN'T BE THERE. HOW DO I SOLVE THIS?)

8   f(x) = x + 3 and g(x) = √x, find g(f(x)).

(g o f)(x) = g ( f(x))

= g (x + 3)

= √(x + 3)   Domain: {x: x ≤ 3}   (IS THIS CORRECT?)

9   f(x) = x - 1  and g(x) = 3/(x-1), find f(g(x)).

(f o g)(x) = f (g(x))

= f [ 3/ (x - 1) ]    Domain: {x: x ≥ 1}   (IS THIS CORRECT?)

FOR THE FOLLOWING EXERCISE I HAVE SOLVED PARTS A AND B, BUT AM TOLD THAT THE ANSWER FOR PART C IS NOT ENOUGH.

10    You go to a local mechanic to get your tires changed.  The tires cost x dollars.  There is a 6% sales tax, but you get a 10% discount.

A    Write a function t(x) for the total purchase amount after taxes but before discounts and fees.

Function with no discount and fees:

tax: 6%

tire cost: x

t(x) = x + 6% of x

t(x) = x + 0.06x

t(x) = 1.06x

B   Write a function d(x) for the total after discounts on purchase amount x but before taxes and fees.

Function with no taxes and fees:

When discount is given after tax, then 10% is deducted from the original cost of the tire:

d(x) = x - 0.10x

C   Does it make a difference in the total price whether the mechanic adds the tax first d(t(x)) or takes the discount first t(d(x))? Do not replace x with a numerical value.  Show the work to support your answer while keeping x in your work.

It does make a difference in the total price if discount is applied first. Out of the whole amount, you would pay 90% of what it costs. When taxes are added to the discounted price, then the total price would be way less than if the taxes were added first and then the discount.

Thank you so much,

## #12 Help Me ! » Composition of Functions » 2022-07-22 01:37:41

Replies: 0

Hello,

Can I get feedback on if these look correct?

1    Given f = { (-1, 8), (3, -1), (-2, 0) } and g =  { (-5, 8), (3, -1), (-1, 0) } .  Find (f o g)(3).  Show steps,

( f o g)(3) = f ( g(3) ) = f(-1) = 3   (IS THIS CORRECT?)

2   Given f = { (-1, 8), (3, -1), (-2, 0) } and g =  { (-5, 8), (3, -1), (-1, 0) } .  Find (g o f)(3). Show steps,

( g o f)(3) = g ( f(3) ) = g(-1) = 3   (IS THIS CORRECT?)

5   f(x) = 15x -12 and g(x) = -15x^2 + 14x - 10, find (f o g)(-1).

( f o g)(-1) = f ( g(-1) )

g(-1) = -15^2 + 14(-1) - 10 = -249

f(-249) = 15(-249) - 12 = -3747

(f o g)(-1) = -3747   (FOR THIS ONE I WAS TOLD THAT -15 IS NOT SQUARED, BUT IN THE G FUNCTION IT IS SQUARED. WHAT AM I SUPPOSED TO CHANGE?)

Is it supposed to be done like this:

(f o g)(-1) = f( g(x))
f( -15^2 + 14x - 10)
15x ( -15^2 + 14x - 10) - 12
-3375x + 210x^2 -150x - 12
= 210^2 -3525x - 12

6    f(x) = -13x2 -13x + 14 and g(x) = -13x - 11, find (g(g(-3)).
(g o g)(-3) = g ( g(-3))

= g ( (-13x - 11) )

= -13 (-13x - 11) -11

= -169x + 143 - 11

= 169x + 132    (THE FEEDBACK WAS THAT FIRST, g(-3)) PUT -3 IN THE G FUNCTION AND THEN SIMPLIFY)

Is it supposed to go like this:

(g o g)(-3) = g ( g(-3))

g(-3) = -13(-3) -11 = 28

(g o g)(-3) = 28

7   f(x) = 2x + 3 and g(x) = –x^2 + 5, find (g o g)(x).

(g o g)(x) = g (g(x))

= g (-x^2 + 5)

= √(-x^2 + 5)

= -x + 5   Domain: {x:x Ð„ R}   (I WAS TOLD THAT THE RADICAL SHOULDN'T BE THERE. HOW DO I SOLVE THIS?)

8   f(x) = x + 3 and g(x) = √x, find g(f(x)).

(g o f)(x) = g ( f(x))

= g (x + 3)

= √(x + 3)   Domain: {x: x ≤ 3}   (IS THIS CORRECT?)

9   f(x) = x - 1  and g(x) = 3/(x-1), find f(g(x)).

(f o g)(x) = f (g(x))

= f [ 3/ (x - 1) ]    Domain: {x: x ≥ 1}   (IS THIS CORRECT?)

FOR THE FOLLOWING EXERCISE I HAVE SOLVED PARTS A AND B, BUT AM TOLD THAT THE ANSWER FOR PART C IS NOT ENOUGH.

10    You go to a local mechanic to get your tires changed.  The tires cost x dollars.  There is a 6% sales tax, but you get a 10% discount.

A    Write a function t(x) for the total purchase amount after taxes but before discounts and fees.

Function with no discount and fees:

tax: 6%

tire cost: x

t(x) = x + 6% of x

t(x) = x + 0.06x

t(x) = 1.06x

B   Write a function d(x) for the total after discounts on purchase amount x but before taxes and fees.

Function with no taxes and fees:

When discount is given after tax, then 10% is deducted from the original cost of the tire:

d(x) = x - 0.10x

C   Does it make a difference in the total price whether the mechanic adds the tax first d(t(x)) or takes the discount first t(d(x))? Do not replace x with a numerical value.  Show the work to support your answer while keeping x in your work.

It does make a difference in the total price if discount is applied first. Out of the whole amount, you would pay 90% of what it costs. When taxes are added to the discounted price, then the total price would be way less than if the taxes were added first and then the discount.

Thank you so much,

## #13 Re: Help Me ! » Solving Quadratic Inequalities » 2022-07-13 20:37:39

Hello,

In this exercise I am told to try the three intervals again. What am I doing wrong?

## #14 Help Me ! » Quadratic Inequalities » 2022-07-13 20:33:33

Replies: 2

Hello,

I have solved this exercise as follows:

x^2 + 49 < 14x

7^2 + 49 < 14(7)

49 + 49 < 98

98 < 98   X

This inequality is not true, because 98 is equal to 98.

What is there more to solve?

Thank you,

## #15 Help Me ! » Solving Quadratic Inequalities » 2022-07-12 01:09:26

Replies: 3

Hi,

Is this the correct way to solve this exercise:

Nathan is a product manager for a home security company.  Through testing and focus groups, he has modeled the equation P = -(x - 32)^2 + 1000 to represent the profit (in thousands) of the price x for a new home security camera.  Find the prices in dollars at which Nathan can make a profit of at least \$471, 000.  Show your work as it is done in the lesson content and include units of measurement..  HINT:  Use 471 as part of the inequality you set up, not 471,000.

- (x - 32)^2 + 1000 = 471
1000 - 471 = (x - 32)^2
529 = (x - 32) (x -32)
529 = x (x - 32) - 32 (x - 32)
529 = x^2 - 32x - 32x + 1024
529 = x^2 - 64x + 1024
529 - (x^2 - 64x + 1024) = 0
529 - x^2 + 64x - 1024 = 0
-x^2 + 64x - 495 = 0
- (x^2 - 64x + 495) = 0
x^2 - 64x + 495 = 0

x = 9 or x = 55

First interval, x < 9, select x = 8
-8^2 + 64(8) - 495 ≥ 471
81 ≥ 471   FALSE

Second interval, 9 < x < 55, select x = 30
2325 ≥ 471   TRUE. x values in that interval are part of the solution

Third interval, x > 55, select x = 56
6225 ≥ 471   TRUE. x values in that interval are part of the solution

ANSWER: 9< x < 55 or x > 55

Is this correct?

## #16 Help Me ! » Solving Quadratic Inequalities » 2022-07-12 00:02:22

Replies: 1

Hello,

I can't understand how to solve this problem:

Nathan is a product manager for a home security company.  Through testing and focus groups, he has modeled the equation P = -(x - 32)2 + 1000 to represent the profit (in thousands) of the price x for a new home security camera.  Find the prices in dollars at which Nathan can make a profit of at least \$471, 000.  Show your work as it is done in the lesson content and include units of measurement..  HINT:  Use 471 as part of the inequality you set up, not 471,000.

## #17 Re: Help Me ! » Solving Quadratic Inequalities » 2022-07-11 20:41:32

Hello,

I also have trouble completing this exercise:

-x^2 - 12x - 32 > 0

Thank you so much,

## #18 Help Me ! » Solving Quadratic Inequalities » 2022-07-10 04:04:31

Replies: 3

Hello,

I can't solve this problem:

Nathan is a product manager for a home security company.  Through testing and focus groups, he has modeled the equation P = -(x - 32)2 + 1000 to represent the profit (in thousands) of the price x for a new home security camera.  Find the prices in dollars at which Nathan can make a profit of at least \$471, 000.  Show your work as it is done in the lesson content and include units of measurement..  HINT:  Use 471 as part of the inequality you set up, not 471,000.

Thank you so much,

## #19 Help Me ! » Quadratic equations » 2022-07-04 04:13:44

Replies: 1

Hello,
I need help with this exercise.

A ball is launched upward at a speed of 20 meters per second (m/s) from a 60-meter tall platform.  The equation for the ball’s height (h in meters) at time t seconds after launch is h = -4.9t2 + 20t + 60.   How long before the ball hits the ground?

Best,

## #20 Re: Help Me ! » Linear Inequalities » 2022-06-10 01:10:39

Hello,

I'm having trouble finding the solution for this:

2x > -4y

## #21 Help Me ! » Linear Inequalities » 2022-06-09 20:26:49

Replies: 4

Hello,

I am having trouble solving this system of inequalities and graphing it:

2x > -4y
4y - 2x < 8

Thank you,

## #22 Re: Help Me ! » Absolute value inequality » 2022-04-03 09:25:15

I am having trouble with this exercise.

4. Which is a factor of  8x^2 + 4x - 24 when it is completely factored?

A. (2x + 3)
B. (x - 2)
C. (x + 2)
D. (x + 3)

## #23 Help Me ! » Absolute value inequality » 2022-04-03 08:57:24

Replies: 6

Hello,

3. Mark is cutting fence posts that are 48 inches tall to sell. He is permitted a 2 inch margin of error. Otherwise, he cannot sell the fence posts. What absolute value inequality models this situation?

A. |x - 48| ≤ 2
B. |x + 48| ≤ 2
C. |x - 2| ≤ 48
D. |x + 2| ≤ 48

The right one is alternative A.

Thank you,

## #24 Re: Help Me ! » Factoring Polynomials » 2021-11-22 11:03:52

Hello!

I am not understanding what I am doing wrong in question 3. Also in questions 4 and 7, how do they continue?

## #25 Re: Help Me ! » Factoring Polynomials » 2021-11-15 09:19:44

Hi,
Do these look correct now?
Thank you!

2. x^9 + 1

(x^3)^3 + 1^3
x^9 + 1 = (x + 1) (x^2 - (x) (1) + 1^2)

(x + 1) (x^2 - x + 1) (x^6 - x^3 + 1)

3. 2m^4 - 2mn^3

2m

2m (m^3) - 2m (m^2 - n^3)

2m (m^3 - m^2 - n^3)

4. 3a^4 + 81a

3a

3a (a^3) + 3a (27)

3a (a^3 + 27)
3a (a^3 + 3^3)

6. a^4 + 1

This can be factored, and leads to the answer (a^2 + 1)^2 -2a^2

7. a^4 – 64

This can be factored with the difference of squares which leads to the answer: (a^2 + 2^3) (a^2 - 2^3)

9.  x^3 + x^2 - x – 1

x^2 (x +1) - 1 (x + 1)

(x + 1) (x^2 - 1)
(x - 1) (x + 1)
(x - 1) (x + 1)^2