Find the domain and range of the inverse of the given function.
-$$f ( x ) = x ^ { 2 } + 3 , x \geq 0$$
A) Domain: $[ 3 , \infty )$; range: $[ 0 , \infty )$
B) Domain and range: all real numbers
C) Domain: $( - \infty , 0 ]$; range: $( - \infty , 3 ]$
D) Domain: $[ 0 , \infty )$; range: $[ 3 , \infty )$

Question

Quizplus · Accepted Answer

The inverse function of $f(x) = x^2 + 3$ for $x \geq 0$ essentially swaps the roles of $x$ and $y$, meaning the original function's range becomes the inverse's domain, and the original function's domain becomes the inverse's range. Since $f(x)$ is defined for $x \geq 0$ and produces outputs starting from 3 upwards, the inverse function's domain is $[3, \infty)$ and its range is $[0, \infty)$.

Find the Domain and Range of the Inverse of the Given