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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 726

Find domain and range

F(x)=(sq(x+2))/((x^2)-9)

M.M.Zeeshan.K

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,462

hi Zeeshan 01

Haven't heard from you for a while. How are you doing?

To answer your question, I made a sketch of the graph.

Firstly, if x < -2 then the square root cannot be computed so that sets a lower limit and determines the domain.

At x = -2 , F(x) = 0

x^2 - 9 = (x-3)(x+3) so there will be vertical asymptotes at -3 and +3, meaning that x tends to either + or minus infinity. The negative one is outside the domain so we needn't consider it. Consider what sign F(x) has as x approaches 3 from above and below. When x > 3 and approaching 3 both the numerator and denominator are + so the curve will tend to + infinity. When x < 3 and approaching 3 the denominator switches to negative so that part of the curve tends to - infinity. That's enough to decide the range.

If you want to view the graph go to https://www.mathsisfun.com/data/functio … 2)/(x^2-9)

Hope that helps,

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob Bundy

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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 726

M.M.Zeeshan.K

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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 726

Domain f(x)= [-2,+infinity)

In this x^2 - 9 = (x-3)(x+3) when x>3 it become positive infinity and when x<3 it becomes negative infinity but i dont want range of denominator i want range of complete function

M.M.Zeeshan.K

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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 726

How?

That's enough to decide the range.

M.M.Zeeshan.K

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,462

Domain f(x)= [-2,+infinity)

Yes, but you must also add x ≠ 3 as there is no value for F(x) at this point. infinity is not regarded as a number.

The range is all the values that F(x) can take. (x-3)(x+3) determines this because when the denominator approaches 3, the denominator tends to zero so the function tends to either + or - infinity. This means that all values occur for F(x) so the range is (-∞ , +∞) If you look at the graph, choose any value for F and draw a horizontal line to try to cut the curve. It is always possible.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob Bundy

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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 726

Domain=[-2,3)U(3,+infinity)

M.M.Zeeshan.K

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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 726

Another way to find range.

M.M.Zeeshan.K

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,462

hi Zeeshan 01

I'm not sure if there is another way. Have a look at this page:

https://www.mathsisfun.com/sets/domain- … omain.html

Somehow you have to find all the possible values that F(x) can have.

You cannot list them in a set as this is (except at x=3) a continuous function. So you have to write the answer in this way:

[lowest values, highest value] although sometimes a square bracket may be replaced with a round bracket to indicate that an endpoint is not included.

I think that considering the graph helps a lot with this. Did you follow the link? It shows that the function is continuous in two sections separated by x=3. It also shows that the function tends to both + and - infinity. Thus we know that the range is all real values of x.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob Bundy

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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 726

I Do not Think Answer is Infinity.

M.M.Zeeshan.K

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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 726

Put some Values in f(x) such as x=100, x=-1 ,x=2 ,x=2.9999 you will see what is range.

M.M.Zeeshan.K

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,462

x F(x)

0 -0.15713484

100 0.00101086

-1 -0.125

2 -0.4

2.99999 -37267.82447

2.999999999 -372677965.4

3.00000001 37267799.89

3.000000001 372677965.5

Using Excel to calculate =SQRT(x+2)/(x^2-9)

As x approaches 3 from below the values of F are getting increasingly big in the negative direction.

As x approaches 3 from above the values of F are getting increasingly big and positive.

Have you looked at the graph?

Are we using the same function ?

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob Bundy

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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 726

(SQRT(x+2))/(x^2-9) square root is on numerator not denominator.

M.M.Zeeshan.K

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,462

hi

There's a lot of brackets there so here's how I analysed the function:

(SQRT(x+2))/((x^2)-9)

(SQRT(x+2)) / ((x^2)-9)

Drop unnecessary brackets

SQRT(x+2) / (x^2-9)

Question 1. Is this the correct function ?

Question 2. Have you looked at the graph linked in post 2 ?

Please answer these questions. If I don't get both answers I shall not be posting again on this thread.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob Bundy

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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 726

Answer1. Yes this is correct function.

Answer2.I have looked the graph.

M.M.Zeeshan.K

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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 726

When we put x= -2 then f(x)=0 , when put x<2 then fx is negative when put x>3 (not 3 ) then f(x) goes to decimal ie

X=4 f(x)=0.349

X=5 f(x)=0.165

X=6 f(x)=0.104

X=20 so f(x)= 0.011

This function is not going to infinity it have some negative values and when x>3 it is coming towards zero.

M.M.Zeeshan.K

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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 726

??

M.M.Zeeshan.K

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,462

The domain is the set of possible 'x' values and the range is the set of possible 'y' values.

You are correct that the curve tends to zero as x tends to infinity but that doesn't tell us the range. You cannot have the value x=3; it is excluded from the domain, but you can get as close to 3 as you like and as you do the function has larger and larger values. There is no value of 'y' that cannot be attained so the range is ( -∞ , ∞ ) Note y = zero is attained at x = -2

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob Bundy

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