Find the domain and range of the inverse of the given function.
-$$f ( x ) = x ^ { 2 } - 7 ; x \geq 0$$
A) Domain: all real numbers; range: $[ 7 , \infty )$
B) Domain: $[ - 7 , \infty )$; range: $[ 0 , \infty )$
C) Domain: all real numbers; range: $[ - 7 , \infty )$
D) Domain and range: all real numbers

Question

Quizplus · Accepted Answer

The original function $f(x) = x^2 - 7$ with $x \geq 0$ has a range of $[-7, \infty)$ because the smallest value it can take is $-7$ (when $x = 0$). For its inverse, the domain and range switch, so the domain of the inverse is $[-7, \infty)$ and the range is $[0, \infty)$ because the original function was defined for $x \geq 0$.

Find the Domain and Range of the Inverse of the Given