Study guides › Level 6 · Master

Working out f(x)

Level 6 · Master · for questions like “f(x) = x² − 3x + 2. What is f(−2)?”

💡 The idea

f(x) is a rule. f(−2) means: put −2 in place of every x.

🪜 The steps

1. Replace every x with the number, in brackets: f(−2) = (−2)² − 3(−2) + 2.
2. Powers first, then multiply, then add and take away.

✏️ Worked examples

1. f(x) = x² − 3x + 2. f(−2)? (−2)² − 3(−2) + 2 = 4 + 6 + 2 = 12.

2. f(x) = 2x² + x − 5. f(3)? 2 × 9 + 3 − 5 = 16.

⚠️ Watch out

• A negative number squared is positive: (−2)² = 4, not −4.
• Minus times minus is plus: −3 × (−2) = +6.

🎯 Try these

1. f(x) = x² + 1. f(−3)?
2. f(x) = 3x − 7. f(5)?
3. f(x) = x² − 4x. f(−1)?

Answers: 1) 10 2) 8 3) 5

This guide is also in the 10MathQ app: tap “📖 Study guide” after a question.