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

Question

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

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Answer 1 · 2017-11-27T06:51:41

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

This is how to figure this out:

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

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

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

Hope this helps!