Q. 78 - Precalculus Enhanced with Graphing Utilities

Question

The domain of a one-to-one function f is $[0,\infty )$, and its range is$[5,\infty )$. State the domain and the range of $f^{-1}$.

Step-by-Step Solution

Answer

If a function f is one to one function and its domain $[0,\infty )$is  and range is $[5,\infty ),$then the domain of its inverse function  will be$[5,\infty )$ and range will  $[0,\infty )$

Step 1. Given data

Function f  is one to one function 

The domain of function f is $[0,\infty )$

The range of function f  is$[5,\infty )$

Step 2. The domain of the inverse function

If a function f is one to one function  

then  Range of function$f=$domain of the inverse function

as Range of function f  is $[5,\infty )$

so the domain of the inverse function will be $[5,\infty )$

Step 3. The Range of the inverse function

If  a function f is one to one function  

then Domain of function f $=$range of inverse function 

As the domain of function f  is $[0,\infty )$

so Range of inverse function will be $[0,\infty )$