Answer:
A pair of linear functions
Explanation:
Given
See comment for options
Required
Which has real numbers as its range and domain
The answer to this is, the linear functions
Take for instance

The above function is real for all values of x
The inverse is calculated as thus:

Replace f(x) with y

Swap y and x

Make y the subject

Divide by m

Replace y with the inverse function

The above function (i.e. the inverse function) is real for all values of x
This is not true for other options