Question

Find the inverse function of the function f.

Answer 1

\[f(x)=x^2-2, x \le0\]

Answer 2

y = x^2 - 2
Solve for x in terms of y
Then interchange x and y. That is put x where there is y and put y where there is x and you will have the inverse function of f(x)

Answer 3

Can someone explain what the \[x \le0\]
means?
I don't really understand restricted domains in general. ):

Answer 4

It means the function is valid only when x is less than or equal to zero.

Answer 5

\[y=x ^{2} -2 \]
then let x=y and y=x
\[x=y ^{2}-2\]
then solve for y
\[y ^{2}=x+2\]
\[y=-\sqrt{x+2}\]

Answer 6

How would I use the restricted domain?

Answer 7

Like... what difference does it make?

Answer 8

when you solve for y
\[y=\sqrt{x+2}\]
\[y=-\sqrt{x+2}\] and your domain is \[x \le 0\]

Answer 9

But if the problem gives you the domain... how do you incorporate it into the function?

Answer 10

For example, let us say a function is y = sqrt(x)

We know that we can't take the square root of a negative number. So we say x must be restricted to zero or greater. We say x >= 0.

So f(x) = sqrt(x) for x >= 0.

Answer 11

If you don't understand me, that's fine... I don't really know what I'm saying either. :P

Answer 12

\[f(x)= 3x ^{3}-2x+4\] find the inverse @ranga

Answer 13

I understand what you guys are saying though.
I just don't understand what to do with the restriction when it's given in the problem...

Answer 14

Does it not change the answer if you just ignored it?

Answer 15

I know how to solve for the inverse without the domain. ^-^

Answer 16

@majdishokri In that case interchange x and y should be the first step. As the individual case warrants...

Answer 17

If there was no restricted domain.... I would know how to solve it. I'm asking if it changes the answer in anyway.

Answer 18

???????????? @ranga

Answer 19

Sorry for being so confusing...

Answer 20

yes the domain changing th solve you should to be attention

Answer 21

Sorry @thewinterfawn Bringing other problems here while trying to answer her question adds to the confusion.

Answer 22

The domain restriction is something to keep in mind. The function is defined only where the domain says it is defined and not anywhere else.
If f(x)=x2−2,x≤0 and I ask you what is f(x) when x = 2 then your answer should be the function is undefined at x = 2 because the function is x^2 - 2 ONLY when x <= 0

Answer 23

okay I understand your explanation.
umm @majdishokri got the answer \[y=-\sqrt{x+2}\]
but my answer didn't have the negative sign..

Answer 24

And if the function were to be graphed it will be to the left side of the Y axis. You wont see any graph or curve on the right hand side of the y axis because on the right hand side x > 0 and the function does not exist in that domain.

Answer 25

I got \[y=\sqrt{x+2}\]

Answer 26

is that wrong?

Answer 27

yes this is a wrong answer because don't match with domain

Answer 28

so how would I use the domain? How do I take the domain in a way that it changes my answer?

Answer 29

I don't know how to use the domain... that's the problem... i know what it means.

Answer 30

ok i can explain

Answer 31

when you finish the solve you have to check your answer and if they matching with the domain

Answer 32

what do i do if it doesn't match?

Answer 33

just delete it

Answer 34

okay... i think i understand it....
Is it like this?
\[y+2=x^2\]
\[\pm \sqrt{y+2}=x\]
\[f^-1(x)=-\sqrt{x+2}\]

Answer 35

you are very smart

Answer 36

omg i actually understood it! thank you so so much.

Answer 37

@majdishokri f(x)=3x3−2x+4 is not an easy function to take the inverse of.