ACT · Intermediate Algebra · Function notation and composition
Question act-q-00356
Hard Multiple choice No calculator
The question
If f(x) = 4x² − 5, what is the value of f(4)?
- 11
- 59
- 60
- -59
Show answer & worked solution
Answer: 59
Worked solution. Substitute x = 4: f(4) = 4 × (4)² − 5 = 4 × 16 − 5 = 64 − 5 = 59.
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. (4)² always equals 16, regardless of the sign of 4.
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 the back end of the section, where the score gradient is steepest. Treat any miss in this subtopic as a signal to drill the subtopic page before you do another full practice test.