# Math Help - Inverse Function

1. ## Inverse Function

How do I find the Inverse of this function?

Let $f(x) = x^2 - 1$ for $x\geq2.$ Find $f^-1(x)$

2. Originally Posted by SHiFT
How do I find the Inverse of this function?

Let $f(x) = x^2 - 1$ for $x\geq2.$ Find $f^-1(x)$
Hi SHIFT,

$f(x)=x^2-1$

$y=x^2-1$

Now, exchange the x and y variables. Then, solve for y.

$f'(x)\Rightarrow x=y^2-1$

$y^2=x-1$

$y=\sqrt{x-1}$

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

For $x \ge 2 , f'(x)=[1, + \infty)$

3. Note: If they'd restricted the original domain to the left-hand half of the parabola, the inverse would have involved the "minus" from the Quadratic Formula, rather than the "plus".