Question

Verify that f and g are inverse functions
f(x)=2x, g(x)=
`(x)/(2)`

Answer 1

see explanation

Explanation:

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

f(g(x)) = g(f(x)) = x

f(g(x)) = f(
`(x)/(2)`) = 2 ×
`(x)/(2)` = x

g(f(x)) = g(2x) =
`(2x)/(2)` = x

Hence

f(x) and g(x) are inverse functions

Answer 2

y=2x

switch x and y

x=2y

solve for y

x/2 =y

this is the same as g(x)