Question

Given the function f(x) = 3(x – 2)2 + 4 with a restricted domain of x ≥ 2, which of the following represents f–1(x)?.

Answer 1

The inverse of the function is $f^{-1}x= \sqrt{\frac{x-4}{3} } + 2$

Domain and Range of functions

Given the function

$f(x) = 3(x - 2)^2 + 4$

To get the inverse, you will follow the same step as shown:

Rewrite the equation to have:

$y= 3(x - 2)^2 + 4$

Replace x with y

$x = 3(y - 2)^2 + 4$

Make y the subject of the formula

$x = 3(y - 2)^2 + 4\\x-4=3(y - 2)^2\\\frac{x-4}{3} = (y-2)^2\\ y-2=\sqrt{\frac{x-4}{3} } \\y = \sqrt{\frac{x-4}{3} } + 2$

Hence the inverse of the function is $f^{-1}x= \sqrt{\frac{x-4}{3} } + 2$

Learn more on inverse of a function here: brainly.com/question/2873333