Question

Any help to solve the inverse function of this problem, please?

Answer 1

part a:

f(x) = 5x + 3

set f(x) equal to y

y = 5x+3

swap x and y

x = 5y + 3

make y the subject

x - 3 = 5y

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

replace y with f^-1(x)

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

part b:

subsitute 8 as x into the inverse function

`{f}^( - 1) (x) = (8 - 3)/(5)`

= 5 ÷ 5

`{f}^( - 1) (8) = 1`

Answer 2

see explanation

Explanation:

(a)

let y = f(x), that is

5x + 3 = y

Rearrange making x the subject

Subtract 3 from both sides

5x = y - 3 ( divide both sides by 5 )

x = (y - 3) / 5, hence

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

(b)

`f^(-1)`(8) = (8 - 3) / 5 = 5/ 5 = 1