Question

I think I'm struggling to find the inverse for this one:

Answer 1

Recall that the derivative of a constant is 0.

$\bf y=x^2-4x+4\implies y=(x-2)^2\implies \stackrel{inverse}{x=(y-2)^2} \\\\\\ \sqrt{x}=y-2\implies \sqrt{x}+2=y\implies x^{\frac{1}{2}}+2=y \\\\\\ \cfrac{1}{2}x^{-\frac{1}{2}}+0=\cfrac{dy}{dx}\implies \cfrac{1}{2}x^{-\frac{1}{2}}=\cfrac{dy}{dx}$