Question

The domain of one-to-one function g is$\left[0,15\right]$, and range is $(0,8)$. State the domain and range oflocalid="1646180141229" $g^{-1}$

Short answer

if a function g is one to one function and its domain is $\left[0,15\right]$and range is localid="1646180210304" $\left(0,8\right)$then the domain of its inverse function$g^{-1}$will be$\left(0,8\right)$and range will be$\left[0,15\right]$

Step-by-step solution

Step 1. Given data    

Functiong 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 functiongis 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 gis 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$\left[0,15\right]$