Find the domain and range of the inverse of the given function.
-$$f ( x ) = - \frac { 1 } { x }$$
A) Domain and range: $( - \infty , 0 ) \cup ( 0 , \infty )$
B) Domain and range; all real numbers
C) Domain: all real numbers; range: $( - \infty , 0 ) \cup ( 0 , \infty )$
D) Domain: $( - \infty , 0 ) \cup ( 0 , \infty )$; range: all real numbers

Question

Quizplus · Accepted Answer

The original function $f(x) = -\frac{1}{x}$ is defined for all real numbers except $x = 0$, which means its range is also all real numbers except $y = 0$. Thus, the inverse function will have a domain and range of $(-\infty, 0) \cup (0, \infty)$, as it essentially swaps the x and y values of the original function.

Find the Domain and Range of the Inverse of the Given