Study guides › Level 8 · Algebra 2

Inverse functions

Level 8 · Algebra 2 · for questions like “f(x) = 3x + 5. What is f⁻¹(20)?”

💡 The idea

f⁻¹ undoes f. f⁻¹(20) asks: which x makes f(x) = 20?

🪜 The steps

1. Set f(x) equal to the number: 3x + 5 = 20.
2. Solve for x: 3x = 15, so x = 5.

✏️ Worked examples

1. f(x) = 3x + 5, f⁻¹(20): 5.

2. f(x) = 4x − 6, f⁻¹(10): 4x = 16, so x = 4.

⚠️ Watch out

• f⁻¹ is not 1 ÷ f. The little −1 means “undo”, not a power.
• Check: f(5) = 20. ✓

🎯 Try these

1. f(x) = 2x + 1, f⁻¹(15)
2. f(x) = 5x − 3, f⁻¹(22)
3. f(x) = 7x + 4, f⁻¹(53)

Answers: 1) 7 2) 5 3) 7

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