f(g(x)) means g first: composition order on the SAT
f(g(2)) asks for g(2) first, then f of that. Compute f(2) first and you'll land exactly on the distractor.
Why it happens
English reads left to right, so f-then-g feels natural. But composition evaluates inside-out, like nested parentheses.
See the trap
f(x) = 2x + 1, g(x) = x². Find f(g(3)).
f(3) = 7, then g(7) = 49.
g(3) = 9, then f(9) = 19.
How to actually fix it
- 1Work from the innermost parentheses outward, always.
- 2Rewrite f(g(3)) as f(□), then fill □ = g(3) before touching f.
- 3Note that f(g(x)) and g(f(x)) rarely match — if your answer appears for both orders, recheck.
FAQ
How is this tested with tables?
The SAT gives f and g as tables and asks f(g(2)) — same inside-out rule, just look up g(2) in its table first.
How do I stop repeating this mistake?
Reading the explanation isn't enough — your brain needs to beat the trap on a fresh question. Practice the skill in the kaoshen.co question bank: miss one and it is logged with the exact error, then brought back to you three days later and again after fourteen.
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