Question

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

f(x) = (x^2 - 4x + 4)
f(x) = (x - 2)^2
f^1(x) = 2 +/- √x

The derivative of 2 + √x is 1/(2x^(1/2)).

The derivative of 2 - √x is -1/(2x^(1/2)).

None of the answer choices seem to reflect both of these findings.

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} \\\\\\ √(x)=y-2\implies √(x)+2=y\implies x^{(1)/(2)}+2=y \\\\\\ \cfrac{1}{2}x^{-(1)/(2)}+0=\cfrac{dy}{dx}\implies \cfrac{1}{2}x^{-(1)/(2)}=\cfrac{dy}{dx}`