on what domain is the function f one-to-one and non-decreasing ? f(x)= (x-2)^2 what is the inverse of restricted to that domain ?

Answer 1

on what domain is the function f one-to-one and non-decreasing ? f(x)= (x-2)^2 what is the inverse of restricted to that domain ?

The domain that f(x)=(x-2)² is non-decreasing is [2,oo).

The inverse of f(x)=(x-2)² is

x=(y-2)²

±√(x)=√[(y-2)²]=y-2

±√(x)+2=y-2+2=y

Thus, y=±√(x)+2

The inverse equation that is restricted to the domain of [2,oo) is y=√(x)+2.