# How do i use composition of functions to determine whether the functions in each pair are inverse functions?

## y=2x-3 and y=2x+3

Nov 27, 2017

f(g(x)) does not equal x, so the functions are not inverses.

#### Explanation:

This is how to figure this out:

Write $y = 2 x - 3$ as $f \left(x\right) = 2 x - 3$, and write $y = 2 x + 3$ as:
$g \left(x\right) = 2 x + 3$

Determine:
$f \left(g \left(x\right)\right) = 2 \left(2 x + 3\right) - 3$
$= 4 x + 3$

So, since f(g(x)) doesn't equal x, the functions are not inverses!

Hope this helps!