Question

Determine whether the following functions are inverses.

F(x)=1/2x-11 and g(x)=2x+22

Answer 1

f(x) and g(x) are inverses

Explanation:

To determine if the 2 functions are inverses

If f(g(x)) = g(f(x)) = x then f(x) and g(x) are inverses

f(g(x)) = f(2x + 22)

=
`(1)/(2)` ( 2x + 22) - 11 = x + 11 - 11 = x

and

g(f(x)) = g(
`(1)/(2)` x - 11 ) + 22

= 2 (
`(1)/(2)` x - 11 ) + 22 = x - 22 + 22 = x

Hence f(x)) and g(x)) are inverses