Find the domain and range of the inverse of the given function.
-$$f ( x ) = \sqrt { x - 4 }$$
A) Domain: $[ 4 , \infty )$; range: $[ 0 , \infty )$
B) Domain and range: all real numbers
C) Domain: $[ 0 , \infty )$; range: $[ 4 , \infty )$
D) Domain: all real numbers; range: $[ 4 , \infty )$

Question

Quizplus · Accepted Answer

The inverse function essentially swaps the roles of the x and y values from the original function. Since $f(x) = \sqrt{x - 4}$ is defined for $x \geq 4$ (making the domain $[4, \infty)$ and the range $[0, \infty)$ because the square root of a number is always non-negative), the inverse function will have its domain as $[0, \infty)$ (the original range) and its range as $[4, \infty)$ (the original domain).

Find the Domain and Range of the Inverse of the Given