Question

Question #810cb

Answer 1

They are not inverses

Explanation:

One way to tell if two functions are inverses of each other is to take one equation, say, `f(x)` and replace all the `x`s with the function of `g(x)`. If the two are inverses of each other, they should simplify to `x`. If they simply to anything other than just `x`, they are not inverses.

`f(g(x))`
`6(6x-1)+1`
`36x-6+1`
`36x-5`
That doesn't equal `x`, so they're not inverses.

Answer 2

If they are inverses, then the following must be true:

`f(g(x))=x` and `g(f(x)) = x`

Explanation:

Given: `f(x)= 6x+1; g(x)=6x-1`

Substitute `g(x)` for every x in `f(x)`

`f(g(x)) = 6g(x)+1`

Substitute the `6x-1` for `g(x)` on the right:

`f(g(x)) = 6(6x-1)+1`

`f(g(x)) = 36x-6+1`

`f(g(x)) = 36x-5`

We may stop and declare that they are not inverses