ACT · Intermediate Algebra · Function notation and composition
Question act-q-00359
Medium Multiple choice No calculator
The question
If f(x) = 2x² − 5, what is the value of f(3)?
- -13
- 1
- 13
- 14
Show answer & worked solution
Answer: 13
Worked solution. Substitute x = 3: f(3) = 2 × (3)² − 5 = 2 × 9 − 5 = 18 − 5 = 13.
Why each wrong choice is wrong. Forgetting to square the input is the dominant error — the linear-substitution distractor catches it.
Test-day tactic. Substitute with parentheses around the input. (3)² always equals 9, regardless of the sign of 3.
About this question type
Items test substitution into function notation, composition, and (occasionally) inverse functions.
You will see a question shaped like this one on roughly every other official ACT form, typically at a moderate position in the section — solidly within the range that separates a 600-band student from a 700-band student. Treat any miss in this subtopic as a signal to drill the subtopic page before you do another full practice test.