Q. 77 - Precalculus Enhanced with Graphing Utilities

Question

The domain of a one-to-one function f is$[5,\infty )$ , and its range is$[-2,\infty )$. 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 is $[5,\infty )$ and range is $[-2,\infty )$ then the domain of its inverse function $f^{-1}$ will be$[-2,\infty )$ and range will $[5,\infty )$

Step 1. Given data

Function f  is one to one function 

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

Range of function f  is$[-2,\infty )$

Step 2. inverse function

If  a function f is one to one function 

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

As the domain of function f is $[5,\infty )$

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

and Range of function $f=$domain of the inverse function $f^{-1}$

as Range of function f  is $[-2,\infty )$

so the domain of the inverse function will be $[-2,\infty )$