Find the domain and range of the inverse of the given function.
-$$f ( x ) = \sqrt [ 3 ] { 9 x - 7 }$$
A) Domain and range: all real numbers
B) Domain: $[ 0 , \infty )$; range: all real numbers
C) Domain: all real numbers; range: $[ 0 , \infty )$
D) Domain: $[ 7 , \infty )$; range: $[ 0 , \infty )$

Question

Quizplus · Accepted Answer

The original function $f(x) = \sqrt[3]{9x - 7}$ is a cube root function, which means it can take all real numbers as inputs (since you can take the cube root of any real number) and can produce all real numbers as outputs. The inverse function essentially "reverses" the roles of inputs and outputs, but since the original function can take and produce all real numbers, its inverse will also have the domain and range of all real numbers.

Find the Domain and Range of the Inverse of the Given