At a Single Number

Sometimes you need one value of a combination, such as $p\left(4\right)-q\left(4\right)$. You do not need the combined rule for that: work out each function at 4, then combine the two numbers.

Take $p\left(x\right) = {x}^{2}-2$ and $q\left(x\right) = 3x+1$. Putting 4 into both rules gives ${4}^{2}-2-\left(3\left(4\right)+1\right)$. Work out each part: p(4) is 14 and q(4) is 13, so the line becomes $14-13$, which is 1.

Combining the rules first gives the same number: ${x}^{2}-3x-3$ at 4 is $16-12-3$, which is 1. Evaluating first is usually shorter, because numbers combine faster than expressions. The brackets around q's rule still matter: they keep all of q(4) subtracted.