Question

What is the inverse of the function below? f(x) = x – 5

Answer 1

ANSWER

The inverse is

$f ^{ - 1} (x) = x + 5$


EXPLANATION

The given function is

$f(x) = x - 5$

To find the inverse of this function, we let

$y = f(x)$

This implies that,

$y = x - 5$


We now interchange x and y to obtain,

$x = y - 5$



We make y the subject again by adding 5 to both sides to get,

$x + 5 = y - 5 + 5$


This implies that,

$x + 5 = y$

or

$y = x + 5$

This new function is the inverse of the given function.

Therefore

$f ^{ - 1} (x) = x + 5$

Answer 2

The inverse of f(x) = x - 5 is y = x + 5