Question

Question #c617d

Answer 1

You could have one function that simplifies into multiplying by `4`, and the other function that simplifies into dividing by `9`.

Explanation:

Say those two functions are `f(x)` and `g(x)`, and that them composed together would be `f(g(x))`.

We have that `f(g(x)) = 4/9 x`

So we could have `f(x) = 4x` and `g(x) = x/9`, so that:

`f(g(x)) = f(x/9) = 4(x/9) = 4/9 x`

Or it could also be that `f(x) = x/9` and `g(x) = 4x`. Due to multiplicative properties, we should get the same result:

`f(g(x)) = f(4x) = (4x)/9 = 4/9 x`

The functions could also be anything else where one must simplify as `4x` and the other as `x/9`. Here's an example:

`f(x) = (8x)/2` and `g(x) = x/sqrt(81)`

Or maybe even it is simply that the two functions should become `4/9 x` together, although it could be a bit risky:

`f(x) = x+3` and `g(x) = (4x - 27)/9`

`f(x) = sin^-1(x)` and `g(x) = sin((4x)/9)`

etc. The possibilities are endless.