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#1 2018-11-10 18:41:48

Zeeshan 01
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Registered: 2016-07-22
Posts: 698

Domain and Range

Find domain and range
F(x)=(sq(x+2))/((x^2)-9)


M.M.Zeeshan.K

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#2 2018-11-10 20:52:46

bob bundy
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Registered: 2010-06-20
Posts: 8,406

Re: Domain and Range

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

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#3 2018-11-11 15:15:08

Zeeshan 01
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Registered: 2016-07-22
Posts: 698

Re: Domain and Range

smile


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#4 2018-11-11 15:21:02

Zeeshan 01
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Registered: 2016-07-22
Posts: 698

Re: Domain and Range

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


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#5 2018-11-11 15:24:41

Zeeshan 01
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Registered: 2016-07-22
Posts: 698

Re: Domain and Range

How?

That's enough to decide the range.


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#6 2018-11-11 20:34:00

bob bundy
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Registered: 2010-06-20
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Re: Domain and Range

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

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#7 2018-11-11 21:08:29

Zeeshan 01
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Registered: 2016-07-22
Posts: 698

Re: Domain and Range

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


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#8 2018-11-11 21:13:49

Zeeshan 01
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Registered: 2016-07-22
Posts: 698

Re: Domain and Range

Another way to find range.


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#9 2018-11-12 20:07:10

bob bundy
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Registered: 2010-06-20
Posts: 8,406

Re: Domain and Range

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

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#10 Yesterday 22:27:52

Zeeshan 01
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Registered: 2016-07-22
Posts: 698

Re: Domain and Range

I Do not Think Answer is Infinity.


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#11 Yesterday 22:34:07

Zeeshan 01
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Registered: 2016-07-22
Posts: 698

Re: Domain and Range

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


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#12 Today 03:43:51

bob bundy
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Registered: 2010-06-20
Posts: 8,406

Re: Domain and Range

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


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

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