Quick answer

Function notation is a short way to name a rule and show its input. The expression f(x) does not mean f multiplied by x.

Read f(x)

Say “f of x.” The letter f names the function, and x represents the input.

Evaluate by substitution

If f(x) = 2x + 1, replace x with 3: f(3) = 2(3) + 1 = 7.

Functions can have other names

g(x) and h(x) are functions too. The name changes, but the idea of mapping each allowed input to one output stays the same.

Worked examples

  • f(x) = x + 4 → f(2) = 6
  • f(x) = 3x → f(-2) = -6
  • g(x) = x² → g(4) = 16

Common mistake to avoid

Do not confuse f(3) with f × 3. Parentheses indicate the function input.

Practice questions

Try these without looking at the answers first. Explain your reasoning aloud or write each step.

  • Question: f(x)=2x; f(6) — Answer: 12
  • Question: g(x)=x+5; g(-2) — Answer: 3
  • Question: h(x)=x²; h(3) — Answer: 9

What to learn next

Review the related lessons linked below, then practice independently. If you make an error, write down which rule you used and why it did not apply.

Explore FitGitt practice.