How do I find the Inverse of this function?
Let $\displaystyle f(x) = x^2 - 1 $ for $\displaystyle x\geq2.$ Find $\displaystyle f^-1(x) $
Hi SHIFT,
$\displaystyle f(x)=x^2-1$
$\displaystyle y=x^2-1$
Now, exchange the x and y variables. Then, solve for y.
$\displaystyle f'(x)\Rightarrow x=y^2-1$
$\displaystyle y^2=x-1$
$\displaystyle y=\sqrt{x-1}$
$\displaystyle f'(x)=\sqrt{x-1}$
For $\displaystyle x \ge 2 , f'(x)=[1, + \infty)$