# Thread: Find the inverse of the function!

1. ## Find the inverse of the function!

Please find the inverse of f(x) = x^2 , x is less than and equal to 0.

I got f^-1(x) = sqrt(x) . But what do I do about the exception "x is less/equal to 0"

Also, the question also states verify that (f o f^-1)(x) = (f^-1 o f)(x) = x . What does this mean? What does the "o" mean? Does it mean to multiply? I've never seen that notation before.

Thank you very much. If anything is unclear please note, and I'll try my best to clarify. Thank you.

2. Originally Posted by ADH
Please find the inverse of f(x) = x^2 , x is less than and equal to 0.

I got f^-1(x) = sqrt(x) . But what do I do about the exception "x is less/equal to 0"

Also, the question also states verify that (f o f^-1)(x) = (f^-1 o f)(x) = x . What does this mean? What does the "o" mean? Does it mean to multiply? I've never seen that notation before.

Thank you very much. If anything is unclear please note, and I'll try my best to clarify. Thank you.
for $\displaystyle f(x) = x^2$ ; $\displaystyle x \le 0$

$\displaystyle f^{-1}(x) = -\sqrt{x}$

the notation in the second part is function composition. another way to write it that might be easier to understand ...

$\displaystyle f[f^{-1}(x)] = f^{-1}[f(x)] = x$

3. So basically it's minus the sqrt of x because x is LESS than/equal to zero?

4. Originally Posted by ADH
So basically it's minus the sqrt of x because x is LESS than/equal to zero?
that's correct ... why?

5. Why not? I just wanted to clarify and understand this thoroughly. It's better than wondering.

6. I'm asking you why it is correct ...