Find the domain and range of the inverse of the given function.
-$$f ( x ) = ( 8 x - 1 ) ^ { 3 }$$
A) Domain: $[ 0 , \infty )$; range: all real numbers
B) Domain and range: all real numbers
C) Domain: $[ 8 , \infty )$; range: $[ 0 , \infty )$
D) Domain: $[ 1 , \infty )$; range: $[ 0 , \infty )$

Question

Quizplus · Accepted Answer

The given function $f(x) = (8x - 1)^3$ is a cubic function, which means it is continuous and differentiable for all real numbers, and its range is all real numbers. Since the inverse function essentially "swaps" the roles of inputs and outputs, the domain and range of the inverse function are also all real numbers.

Find the Domain and Range of the Inverse of the Given