Question

Which of the pairs of functions and their inverses will always have a domain and range of all real numbers?

Answer 1

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

`f(x) = mx + b`

The above function is real for all values of x

The inverse is calculated as thus:

`f(x) = mx + b`

Replace f(x) with y

`y = mx + b`

Swap y and x

`x = my + b`

Make y the subject

`my = x - b`

Divide by m

`y = (x - b)/(m)`

Replace y with the inverse function

`f^(-1)(x) = (x - b)/(m)`

The above function (i.e. the inverse function) is real for all values of x

This is not true for other options