Order Matters

Swap the order of a composition and you usually get a different answer. Take $f\left(x\right) = x+2$ and $g\left(x\right) = {x}^{2}$, with the input 3. $g\left(f\left(3\right)\right)$ adds first: f(3) is 5, then g(5) is 25. $f\left(g\left(3\right)\right)$ squares first: g(3) is 9, then f(9) is 11.

Adding then squaring is not squaring then adding, so the results differ. As rules, $g\left(f\left(x\right)\right) = {\left(x+2\right)}^{2}$ while $f\left(g\left(x\right)\right) = {x}^{2}+2$.

So read a composition from the inside out every time. The innermost call is the one you work out first, whatever its letter, and the letter written first is the one that acts last.