Find the domain and range of the inverse of the given function.
-$$f ( x ) = \sqrt { x - 2 }$$
A) Domain: $[ 0 , \infty )$; range: $[ 2 , \infty )$
B) Domain and range: all real numbers
C) Domain: $[ 2 , \infty )$; range: $[ 0 , \infty )$
D) Domain: all real numbers; range: $[ 2 , \infty )$

Question

Quizplus · Accepted Answer

The domain of the original function $f(x) = \sqrt{x - 2}$ is $[2, \infty)$ because the expression under the square root must be non-negative. The range of this function is $[0, \infty)$ because the square root function outputs non-negative values. For the inverse function, the domain and range swap, so the domain becomes $[0, \infty)$ and the range becomes $[2, \infty)$.

Find the Domain and Range of the Inverse of the Given