Question

Which function is the inverse of function f?

Answer 1

the inverse of a function

steps to find the inverse of a function

step 1: replace f(x) with y

step 2: replace all x's with y's and y's with x's

step 3: solve for y

step 4: replace y with $f^{-1}(x)$, the ineverse of f(x) or whatever function name

given $f(x)=9x^2-12$

step 1: replace f(x) with y

$y=9x^2-12$

step 2: replace all x's with y's and y's with x's

$x=9y^2-12$

step 3: solve for y

$x=9y^2-12$

$x+12=9y^2$

$\frac{x+12}{9}=y^2$

$\sqrt{\pm \frac{x+12}{9}}=y$

$y=\frac{\pm \sqrt{x+12}}{3}$

step 4: replace y with function name

here's where we just match which one matches $inverse=\frac{\pm \sqrt{x+12}}{3}$

that would be A