How do you write y=31+x2 as a composition of two simpler functions?

Let ${\displaystyle g\left(x\right)}$ be the first thing we do if we knew ${\displaystyle x}$ and started to calculate:
${\displaystyle g\left(x\right)=x^2}$
Now ${\displaystyle f}$ will be the rest of the calculation we would do (after we found ${\displaystyle x^2}$)
It may be easier to think about if we gave ${\displaystyle g\left(x\right)}$ a temporary name, say ${\displaystyle g\left(x\right)=u}$
So we see that ${\displaystyle y=3\sqrt{1+u}}$
So ${\displaystyle f\left(u\right)=3\sqrt{1+u}}$ and that tells us we want:
${\displaystyle f\left(x\right)=3\sqrt{1+x}}$
Another answer is to letf ${\displaystyle \left(x\right)}$ be the last thing we would do in calculating ${\displaystyle y}$.
So let ${\displaystyle f\left(x\right)=3x}$
To get ${\displaystyle y=f\left(g\left(x\right)\right)}$ we need ${\displaystyle 3g\left(x\right)=y}$
So let ${\displaystyle g\left(x\right)=\sqrt{1+x^2}}$

Define these functions:
${\displaystyle g\left(x\right)=1+x^2}$
${\displaystyle f\left(x\right)=3\sqrt{x}}$
Then:
${\displaystyle y\left(x\right)=f\left(g\left(x\right)\right)}$