Question

What is the inverse of the function below? f(x) = 5x - 2

A. f -1(x) = x - 2/ 5
B. f -1(x) = x + 2 / 5
C. f -1(x) = -2 + 5x
D. f -1(x) = -5x + 2

Answer 1

B. f -1(x) = x + 2 / 5

`f^(-1)(x)=(x+2)/(5)`

Explanation:

To find the inverse of a function we need to interchange x and y an solve for y.

Since
`f(x)=y`, then

`f(x)=5x-2`

`y=5x-2`

`x=5y-2`

Add 2 to both sides

`x+2=5y-2+2`

`x+2=5y`

Divide both sides by 5

`(x+2)/(5)=(5y)/(5)`

`(x+2)/(5)=y`

`y=(x+2)/(5)`

`f^(-1)(x)=(x+2)/(5)`

We can conclude that the correct answer is B. f -1(x) = x + 2 / 5