SAT functions: f(2) means substitute, then finish the arithmetic
f(x) = 4x³ − 9, find f(3). You wrote 4·3³ − 9, which is right, and then answered 27 or 1,719 — each one operation out of order away from the setup you already had.
Why it happens
Substitution feels like the hard part, so attention drops the moment it is done. But the exponent and the coefficient still have to be applied in the right order, and the answer choices are built from the plausible wrong orders — cubing after multiplying, or adding before multiplying.
See the trap
f(x) = 4x³ − 9. Find f(3).
(4 · 3)³ − 9 = 1,719, or 4 · 3 · 3 − 9 = 27 — the coefficient pulled inside the exponent, or the exponent read as a third factor.
3³ = 27 first, then 4 · 27 = 108, then − 9 = 99.
How to actually fix it
- 1Rewrite with the input in brackets: f(2) = 7(2)³ + 5. The brackets stop the coefficient from creeping inside the exponent.
- 2Evaluate the power before the coefficient, every time.
- 3Do the addition last, and check that your answer is not simply one of the intermediate values.
Practice this trap · 13 real questions
Each of these is a question from the free bank that turns on the mistake above — the trap is the reason its wrong answer looks right. Easiest first.
Showing 8 of 13. Keep going in Advanced Math →
FAQ
What about being given the output and asked for the input instead?
Same two steps in reverse: undo the addition, then undo the coefficient, then undo the power. The trap is identical — stopping one operation early and answering with an intermediate value that is sitting in the choices.
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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