Find the domain and range of the inverse of the given function.
-$$f ( x ) = \frac { 8 } { x ^ { 2 } + 1 } , x \geq 0$$
A) Domain: $( - \infty , 0 \}$; range: $[ - 8,0 )$
B) Domain: $[ 0 , \infty )$; range: $( 0,8 ]$
C) Domain: $( 0,8 ]$; range: $[ 0 , \infty )$
D) Domain and range: $[ 0 , \infty )$

Question

Quizplus · Accepted Answer

The original function $f(x) = \frac{8}{x^2 + 1}$ is defined for $x \geq 0$, and its output decreases as $x$ increases, approaching 0 but never reaching it, and is 8 when $x = 0$. Thus, for the inverse function, the domain (possible outputs of the original function) is $(0, 8]$ and the range (inputs of the original function, which become the outputs of the inverse) is $[0, \infty)$.

Find the Domain and Range of the Inverse of the Given