Question

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

Answer 1

Answer:

A pair of linear functions

Step-by-step 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

$y = \frac{x - b}{m}$

Replace y with the inverse function

$f^{-1}(x) = \frac{x - b}{m}$

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

This is not true for other options