# Thread: Find the Inverse Function

1. ## Find the Inverse Function

Find the inverse of the function f(x) = sqrt{r^2 - x^2}, where 0 < or = to x < or = to r

2. Hello !
Originally Posted by magentarita
Find the inverse of the function f(x) = sqrt{r^2 - x^2}, where 0 < or = to x < or = to r
Why are you stuck ? As $\displaystyle f$ is a bijection on $\displaystyle [0,r]$ (Can you show this ?) its inverse function exists. Let $\displaystyle y=f(x)$ : we're asked to find the inverse function of $\displaystyle f$ that is the function $\displaystyle g$ such that $\displaystyle x=g(y)$. This can simply be done by solving $\displaystyle y=\sqrt{r^2-x^2}$ for $\displaystyle x$ :

\displaystyle \begin{aligned} y=\sqrt{r^2-x^2} & \Longleftrightarrow y^2=r^2-x^2\\ &\Longleftrightarrow x^2=\ldots\\ &\Longleftrightarrow x=\ldots \end{aligned}

hence the inverse function of $\displaystyle f$ is ...

3. ## Bijection???

What is bijection? Our teacher never used that word in class.

4. Bijection means being both one to one and onto.

5. ## nikhil

nikhil:

You said:

"Bijection means being both one to one and onto."

This statement is not too clear.

Can you break it down a little more for those of us who are not math majors?

6. Originally Posted by magentarita
nikhil:

You said:

"Bijection means being both one to one and onto."

This statement is not too clear.

Can you break it down a little more for those of us who are not math majors?
One-to-one and Onto Functions

7. Originally Posted by magentarita
nikhil:

You said:

"Bijection means being both one to one and onto."

This statement is not too clear.

Can you break it down a little more for those of us who are not math majors?
1) one to one
it means each element of domain will have a unique image in codomain.no two elements of domain can have the same image in codomain.
2) onto
it means each element of codomain will surely have a preimage in the domain.no element of codomain will left unlinked with element of domain.
I hope this helps.if still there is any problem then you may ask it freely.

8. ## Finally...

I finally get it.

Thanks