Question

How do you determine the three functions f, g, and h such that `(f o g o h)(x) = sin^2(x+1)`?

Answer 1

Observe what is being done to `x` to find that
`h(x) = x+1`
`g(x) = sin(x)`
`f(x) = x^2`

Explanation:

Let's look at what we're doing to `x` in `sin^2(x+1)`, and what order it is being done in.

1. We add `1`.
2. We take the sine of the result of step 1.
3. We square the result of step 2.

Then, remembering that when applying `f@g@h` we start with `h` and then work to the left, the functions must be

`h(x) = x+1`
`g(x) = sin(x)`
`f(x) = x^2`