Want to actually learn this — with audio, spaced repetition and progress tracking?

Mathematics · Year 11 (Methods 1–2) · Chapter 1

What f(x) means

Practice

f(x) = 2x + 1 → f(3): 7 — feed 3 in: 2(3) + 1
f(x) = x² → f(5): 25
g(x) = 3x − 2 → g(0): −2
f(x) = 2x + 1 → f(−1): −1
f(x) = x² → f(−3): 9 — (−3)² is positive
h(x) = 10 − x → h(4): 6
f(x) means: the output of machine f for input x — NOT f × x
f(x) = 2x + 1: solve f(x) = 9: x = 4
domain: the set of allowed inputs
range: the set of possible outputs

Easy questions

f(x) = 2x + 1 → f(3): 7
f(x) = x² → f(4): 16
g(x) = x − 5 → g(5): 0
f(x) = 3x → f(0): 0
h(x) = 10 − x → h(3): 7

Medium questions

f(x) = 2x + 1 → f(−2): −3
f(x) = x² → f(−3): 9
f(x) = x² + 1 → f(2): 5
g(x) = 3x − 2: solve g(x) = 7: x = 3
f(x) = 2x → f(a + 1): 2a + 2

Hard questions

f(x) = x² − 2x → f(3): 3 — 9 minus 6
f(x) = 2x + 1 → f(f(1)): 7 — f(1) = 3, then f(3) = 7
f(x) = x²: solve f(x) = 49: x = 7 or x = −7
f(x) = x² → f(x + 1): (x+1)² = x² + 2x + 1
Why is f(3) not 'f times 3'?: f isn't a number — it's the machine's name; the brackets mean 'feed this in'

Lesson

A function is a machine

A function is a machine: numbers go in, a rule runs, numbers come out. f(x) = 2x + 1 names the machine f and states its rule: double the input, add one. f(3) doesn't multiply anything — it means 'feed 3 into f': f(3) = 2(3) + 1 = 7. The brackets are the machine's mouth, not a multiplication. It's an unfortunate notation clash, and everyone trips on it exactly once. Two habits keep the machine honest: wrap negative inputs in brackets before running the rule — f(−1) = 2(−1) + 1 = −1, and for f(x) = x², f(−3) = (−3)² = 9 — and read questions in machine language: 'solve f(x) = 9' asks WHICH input makes the output 9.

f(x) = 2x + 1: f(3) = 2(3) + 1 = 7. Input 3, output 7.
f(−1) = 2(−1) + 1 = −1 — brackets around the negative first.
f(x) = x²: f(−3) = (−3)² = 9.
Solve f(x) = 9: 2x + 1 = 9 → x = 4 — find the input that gives 9.

Want to actually learn this — with audio, spaced repetition and progress tracking?

Study in the app →