Composition of functions
SAT glossary · Math
Definition
F(g(x)): apply g first, then f. Order matters; f(g(x)) ̸= g(f(x)) in general, and reversing the order is the standard trap.
Composition of functions in plain English
Composition of functions just means feeding the output of one function directly into another function as its input — like an assembly line where one machine's product becomes the next machine's raw material. f(g(x)) means: first run x through machine g, then take whatever comes out and run THAT through machine f. The order is everything here — running g then f almost always gives a totally different result than running f then g, so f(g(x)) is generally not equal to g(f(x)). The most common mistake is accidentally reversing which machine goes first, which is exactly the wrong answer the test likes to include as a trap.
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