Q. 79 - Precalculus Enhanced with Graphing Utilities

Question

The domain of a one-to-one function g is$(-\infty ,0)$ , and its range is$[0,\infty )$. State the domain and the range of$g^{-1}$ .

Step-by-Step Solution

Answer

If a function g is one to one function and its domain is$(-\infty ,0)$  and range$[0,\infty )$ is then the domain of its inverse function $g^{-1}$ will be $[0,\infty )$and range will  $(-\infty ,0)$

Step 1. Given data

Function g is one to one function  

The domain of function g is $(-\infty ,0)$

The range of function g is$[0,\infty )$

Step 2. The domain of the inverse function

If  a function g is one to one function  

then  Range of function $g=$domain of the inverse function $g^{-1}$

as Range of function g  is $[0,\infty )$

so the domain of the inverse function $g^{-1}$ will be $[0,\infty )$

Step 3. The Range of the inverse function

If  a function g is one to one function  

then Domain of function g$=$ range of inverse function $g^{-1}$

As the domain of function g is $(-\infty ,0)$

so Range of inverse function$g^{-1}$ will be $(-\infty ,0)$