Question

F: x 5 – 3x. (a) Find f(–1). (b) Find f –1(x).

Answer 1

`f(-1) = 8`

`f^(-1)(x) = (5)/(3) - (x)/(3)`

Explanation:

Given

`f(x) = 5 - 3x`

Required

`f(-1)` and
`f^(-1)(x)`

Solving for f(-1)

Substitute -1 for x in
`f(x) = 5 - 3x`

`f(-1) = 5 - 3(-1)`

`f(-1) = 5 + 3`

`f(-1) = 8`

Solving for
`f^(-1)(x)`

Let y = f(x)

`y = 5 - 3x`

Interchange the position of x and y

`x = 5 - 3y`

Make y the subject of formula (add 3y to both sides)

`3y + x = 5 - 3y + 3y`

`3y + x = 5`

Subtract x from both sides

`3y + x - x = 5 - x`

`3y = 5 - x`

Divide through by 3

`(3y)/(3) = (5)/(3) - (x)/(3)`

`y = (5)/(3) - (x)/(3)`

Replace y with
`f^(-1)(x)`

`f^(-1)(x) = (5)/(3) - (x)/(3)`