Function notation
SAT glossary · Math
Definition
f(x) is not f times x — it is the output of the machine f fed the input x, and whatever sits inside the parentheses is substituted for every x in the definition. Most function-notation errors are dropped parentheses: f(a+1) = (a+1)^2 - 3(a+1).
Function notation in plain English
Function notation like f(x) can look like multiplication (f times x), but it's actually completely different — it means 'the output of machine f when you feed it the input x.' Whatever expression sits inside those parentheses gets substituted in for EVERY single copy of the variable in the function's definition. The single most common way students slip up here is dropping parentheses when substituting something more complicated than a lone variable — for instance, f(a+1) means every 'x' in the original definition gets replaced by the WHOLE expression (a+1), in parentheses, everywhere it appears, like (a+1)^2 - 3(a+1) — not just tacked onto part of the formula.
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