Question

Given f(x) = 1/x+1 and g(x)--2x algebraically find the following

Answer 1

`f^(-1)(x) = (1)/(x) - 1`

`g^(-1)(x) = (x^2)/(2)`

Explanation:

For f(x):

Let y = f(x) =
`(1)/(x+1)`

Replace x with y:

`x=(1)/(y+1)`

Solve for y:

`y+1 = (1)/(x)`

`y = (1)/(x) - 1 = f^(-1)(x)`

For g(x)

Let y = g(x) =
`√(2x)`

Replace x with y

`x=√(2y)`

Solve for y

`x^2 = 2y\\y = (x^2)/(2)`=
`g^(-1)(x)`