Question

Which of the following pairs of functions are inverses of each other

Answer 1

`f(x) = 5x -11` and
`g(x) = (x + 11)/(5)`

Explanation:

Required

The inverse pairs

Solving (a):

`f(x) = 5x -11`
`g(x) = (x + 11)/(5)`

Calculate the inverse of f(x)

`f(x) = 5x -11`

Replace f(x) with y

`y = 5x - 11`

Swap x and y

`x = 5y - 11`

Solve for y

`5y = x + 11`

`y = (x + 11)/(5)`

So, we have:

`g(x) = (x + 11)/(5)`

Hence, f(x) and g(x) in (a) are inverse functions

Others are not