Question

Two functions f and g are defined on the set R of real numbers by f(x) = 2x - 1 and g(x) =x² + 1. Find the value of
`f^(-1)`og (3)

Answer 1

`(11)/(2)`

Explanation:

To obtain the inverse of f(x)

let y = f(x) and rearrange making x the subject, that is

y = 2x - 1 ( add 1 to both sides )

y + 1 = 2x ( divide both sides by 2 )

`(y+1)/(2)` = x

Change y back into terms of x with x =
`f^(-1)`(x) , thus

`f^(-1)`(x) =
`(x+1)/(2)`

Evaluate g(3) and substitute the value obtained into
`f^(-1)`(x)

g(3) = 3² + 1 = 9 + 1 = 10, then

`f^(-1)` (10) =
`(10+1)/(2)` =
`(11)/(2)`