Question

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

Answer 1

we are given that

`f(x)=√(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)`