Q. 80 - Precalculus Enhanced with Graphing Utilities

Question

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

Step-by-Step Solution

Answer

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

Step 1. Given data

Function g is one to one function  

The domain of function g is $\left[0,15\right]$

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

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 $\left(0,8\right)$

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

Step 3. The Range of the inverse function

If  a function g is one to one function  

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

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

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