Question

1. determine if the functions are inverse functions

f(x) = x+6
g(x) = x-6
2. determine if the functions are inverse functions
f(x) = -3x-9
g(x) = -1/3x-3

Answer 1

Question 1

The function
`f(x) = x + 6` is one-to-one, so it does have an inverse.

The inverse of +6 is -6, so
`f^(-1)(x)=x-6`

Therefore, g(x) is the inverse of f(x).

Question 2

The function
`f(x) = -3x -9` is one-to-one, so it does have an inverse.

To find the inverse, replace f(x) with y:

`\implies y = -3x -9`

Rearrange the equation to make x the subject:

`\implies y+9= -3x`

`\implies x=-\frac13(y+9)`

`\implies x=-\frac13y-3`

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

`\implies f^(-1)(x)=-\frac13x-3`

Therefore, g(x) is the inverse of f(x).