Question

How do you write `y = 3sqrt(1 + x^2)` as a composition of two simpler functions?

Answer 1

Define these functions:
`g(x)=1+x^2`
`f(x)=3sqrtx`

Then:
`y(x)=f(g(x))`

Answer 2

There is more than one way to do this.

Explanation:

Adrian D has given one answer, here are two more:

Let `g(x)` be the first thing we do if we knew `x` and started to calculate:

`g(x) = x^2" "`

Now `f` will be the rest of the calculation we would do (after we found `x^2`)

It may be easier to think about if we gave `g(x)` a temporary name, say `g(x)=u`

So we see that `y = 3sqrt(1+u)`

So `f(u) = 3sqrt(1+u)` and that tells us we want:

`f(x) = 3sqrt(1+x)`

Another answer is to let `f(x)` be the last thing we would do in calculating `y`.

So let `f(x) = 3x`

To get `y = f(g(x))` we need `3g(x) = y`

So let `g(x) = sqrt(1+x^2)`