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

Zeeshan 01
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Registered: 2016-07-22
Posts: 717

### 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
Registered: 2010-06-20
Posts: 8,442

### Re: Domain and Range

hi Zeeshan 01

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

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

Zeeshan 01
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Registered: 2016-07-22
Posts: 717

M.M.Zeeshan.K

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

Zeeshan 01
Member
Registered: 2016-07-22
Posts: 717

### 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

M.M.Zeeshan.K

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

Zeeshan 01
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Registered: 2016-07-22
Posts: 717

### Re: Domain and Range

How?

That's enough to decide the range.

M.M.Zeeshan.K

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

bob bundy
Registered: 2010-06-20
Posts: 8,442

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

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

Zeeshan 01
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Registered: 2016-07-22
Posts: 717

### Re: Domain and Range

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

M.M.Zeeshan.K

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

Zeeshan 01
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Registered: 2016-07-22
Posts: 717

### Re: Domain and Range

Another way to find range.

M.M.Zeeshan.K

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

bob bundy
Registered: 2010-06-20
Posts: 8,442

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

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## #10 2018-11-13 22:27:52

Zeeshan 01
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Registered: 2016-07-22
Posts: 717

### Re: Domain and Range

I Do not Think Answer is Infinity.

M.M.Zeeshan.K

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## #11 2018-11-13 22:34:07

Zeeshan 01
Member
Registered: 2016-07-22
Posts: 717

### 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.

M.M.Zeeshan.K

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## #12 2018-11-14 03:43:51

bob bundy
Registered: 2010-06-20
Posts: 8,442

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

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## #13 2018-11-14 15:22:17

Zeeshan 01
Member
Registered: 2016-07-22
Posts: 717

### Re: Domain and Range

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

M.M.Zeeshan.K

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## #14 2018-11-14 21:36:33

bob bundy
Registered: 2010-06-20
Posts: 8,442

### Re: Domain and Range

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 ?

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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## #15 2018-11-14 21:43:08

Zeeshan 01
Member
Registered: 2016-07-22
Posts: 717

### Re: Domain and Range

Answer1. Yes this is correct function.

M.M.Zeeshan.K

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## #16 2018-11-14 21:51:46

Zeeshan 01
Member
Registered: 2016-07-22
Posts: 717

### Re: Domain and Range

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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## #17 2018-11-17 18:00:45

Zeeshan 01
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Registered: 2016-07-22
Posts: 717

??

M.M.Zeeshan.K

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## #18 2018-11-17 20:49:45

bob bundy
Registered: 2010-06-20
Posts: 8,442

### Re: Domain and Range

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

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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