Question

Find the domain and range of
\[f(x)=\frac{1}{(x+3)^2}\]

Answer 1

domain : all real values except -3

Answer 2

My textbook has the answer: \[[0, \infty)\] But I don't know how they got that.

Answer 3

That is interval notation.

Answer 4

the answer u give is range or domain

Answer 5

This means ---> all values from 0 to infinite, but not including infinite.

Answer 6

The domain would look like \((-\infty,-4]\cup [-2,+\infty)\)

Answer 7

Just make the range (1/-infinite,1/-4]U[1/-2, +1/infinite)

Answer 8

oops

Answer 9

@ParthKohli ur domain leaving all real values close to -3.
i

Answer 10

Oops i know

Answer 11

\([0,{1 \over +\infty})\) is the range as the square of any negative number is positive!

Answer 12

Wait, \((0,\infty)\) is correct.

Answer 13

Yes.

Answer 14

I only learnt how to find the range from a graph and not equation... does it call for different working?

Answer 15

range is correct @ParthKohli but domain is (\[(-\infty ,\infty)\]) except -3

Answer 16

That's what I wrote.. see it again

Answer 17

What is the working to find the range because I am not able to find it by just looking at it.

Answer 18

@ParthKohli ur domain : (−∞,−4]∪[−2,+∞)
but this is leaving many numbers like -3.11 etc

Answer 19

this leaves all values from -2 to -2.9999 and -3.00001 to -3.99999

Answer 20

I know how to find the domain can someone please tell me how to calculate and find range or how you all got it :'(

Answer 21

@purplec16 look at the fun..
the denominator should not be zero for this func to valid...so domain is all values except -3
and it can be easily seen this func generates only +ve values and hence 0 to infinity is the range

Answer 22

@himanshu31 What happens if the graph generates negative values or complex numbers then what will my range be?

Answer 23

u have to include all these numbers but i dont use graph method for these simple func..look at the func and start thinking what values it can made

Answer 24

okay, thanks so much everyone!!