Q. 80 - Precalculus Enhanced with Graphing Utilities

Question

The domain of a one-to-one function g is$[0,15]$ , and its range is$(0,8)$. State the domain and the range of$g^{-1}$ .

Step-by-Step Solution

Answer

If a function f is one to one function and its domain is $[0,15]$ and range is$(0,8)$ then the domain of its inverse function $g^{-1}$ will be$(0,8)$ and range will  $[0,15]$

Step 1. Given data

Function g is one to one function  

The domain of function g is $[0,15]$

The range of function g is$(0,8)$

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 $(0,8)$

so the domain of the inverse function$g^{-1}$ will be $(0,8)$

Step 3. The Range of the inverse function

If  a function g is one to one function  

then  

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

As the domain of function g  is $[0,15]$

so Range of inverse function$g^{-1}$ will be $[0,15]$