Question

Given f(x) = 4(x - 2)³ + 2, classify each statement about f-¹ (x) as true or false.

Answer 1

Explanation:

`f(x)=4(x-2)^3+2\\The inverse of the function is,\\Let y=f(x) then x=f^-1(y)\\y=f(x)=4(x-2)^3+2\\y-2=4(x-2)^3\\(1/4)(y-2)=(x-2)^3\\x-2=((1/4)(y-2))^(1/3)\\x=2+((1/4)(y-2))^(1/3)\\f^-1(y)=2+((1/4)(y-2))^(1/3)\\f^-1(x)=2+((1/4)(x-2))^(1/3)\`