Question

Without finding the inverse of the function determine the range of the inverse of f(x)=sqrt x-4

Answer 1

Solution:

we are given that

$f(x)=\sqrt{x-4}$

we have been asked to find range of the inverse of f(x).Without finding the inverse of the function.

Range of inverse of function=Domain of the function.

Here domain of the given function can be defined as below

The given function will be defined only for

$x-4\geq 0\\ \\ x\geq 4$

Hence the domain of f(x) is $[4, \infty)$

Hence the range of the inverse of the given function is $[4, \infty)$