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Function Notation for IGCSE Maths

Understanding f(x) notation and evaluating functions. This subtopic is part of Functions in the Cambridge IGCSE Mathematics 0580 syllabus (both Core and Extended tiers). Understanding function notatio

What You Need to Know

Understanding f(x) notation and evaluating functions. This subtopic is part of Functions in the Cambridge IGCSE Mathematics 0580 syllabus (both Core and Extended tiers). Understanding function notation is essential for achieving a strong grade in your IGCSE Maths exam.

Understanding Function Notation

Function notation f(x) means 'the output when x is the input'. For example, if f(x) = 3x − 5, then f(4) means substitute x = 4: f(4) = 3(4) − 5 = 7. IGCSE 0580 tests: evaluating f(a) for a number or expression, finding x when f(x) = k (reversing the process), and working with two separate functions in the same question. It appears in both Core and Extended papers.

Step-by-Step Method

  1. 1

    Write out the function definition

    State the rule, e.g. f(x) = 2x² − 3x + 1. Keep this visible throughout your working.

  2. 2

    Substitute the given input

    Replace every x with the input value (number or expression). Use brackets around the substituted value.

  3. 3

    Simplify

    Evaluate the arithmetic or algebra step by step. Show each stage.

  4. 4

    Solve f(x) = k when needed

    Set the function equal to k and solve the resulting equation. For linear f(x), rearrange. For quadratic f(x), solve the quadratic.

  5. 5

    Check by substitution

    Verify your answer by substituting back into the original function.

Worked Example

Question

f(x) = x² − 4x + 3. (a) Find f(−2). (b) Find the values of x for which f(x) = 0.

Solution

Part (a): f(−2) = (−2)² − 4(−2) + 3 = 4 + 8 + 3 = 15 Part (b): x² − 4x + 3 = 0 Factorise: (x − 1)(x − 3) = 0 x = 1 or x = 3 Answers: (a) f(−2) = 15 (b) x = 1 or x = 3

Exam Tips for Function Notation

  • Always use brackets when substituting a negative number: f(−3) = (−3)² not −3².
  • f(x) = 0 asks you to solve an equation; f(0) asks you to evaluate a number — read the question carefully.
  • When two functions are in the same question, use their names (f and g) clearly to avoid confusing them.
  • For f(x) = k with a quadratic, rearrange to ax²+bx+c = 0 before attempting to solve.

Practice Questions

Q1: g(x) = 5x − 3. Find g(0), g(3) and the value of x for which g(x) = 22.

Show hint

g(0)=−3, g(3)=12. For g(x)=22: 5x−3=22 → 5x=25 → x=5.

Q2: h(x) = 1/(x − 2). Find h(5) and explain why h(2) is undefined.

Show hint

h(5) = 1/3. h(2) = 1/0, which is undefined (division by zero).

Q3: f(x) = 2x + 1 and g(x) = x². Find the values of x for which f(x) = g(x).

Show hint

Set 2x + 1 = x² → x² − 2x − 1 = 0. Use quadratic formula.

Frequently Asked Questions

What is function notation in IGCSE Maths?

Understanding f(x) notation and evaluating functions.

Is function notation in the Core or Extended syllabus?

Function Notation is part of the Core and Extended syllabus for IGCSE Mathematics 0580.

How do I revise function notation effectively?

Start with the revision notes to understand key concepts, then work through the worked examples step by step. Finally, practise past paper questions under timed conditions. Teacher Rig recommends spending focused revision sessions on function notation rather than trying to cover everything at once.

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