Question

Find the inverse of the function and then determine whether the inverse is a function.

Answer 1

as you already know, we start off by doing a quick switcheroo on the variables, and then we solve for y to get the inverse,

$\bf y=x^2+4\implies \stackrel{switcheroo}{x = y^2+4}\implies x-4=y^2\implies \pm\sqrt{x-4}=\stackrel{f^{-1}(x)}{y}$

and if you run a vertical line test on that expression, you'll find that it doesn't pass it, meaning is not a function.

Answer 2

X^2=y-4
x= +-√y-4 so f(x)=+-√x-4 it s not a function because squaring is not invertible you just showed what inverse should of the function x^2+4 "should " look like

√ x-4 >=0 and
-√x-4 is not >=0 and y= √x-4 and -√x-4 is not equal to √x-4 these are just possible values but only the first one could be a function