Study guides › Level 8 · Algebra 2

Combining functions: f(g(x))

Level 8 · Algebra 2 · for questions like “f(x) = 2x + 3 and g(x) = x² + 1. What is f(g(2))?”

💡 The idea

f(g(x)) means: put x into g first, then put that answer into f. Work from the inside out.

🪜 The steps

1. Inside: g(2) = 2² + 1 = 5.
2. Outside: f(5) = 2 × 5 + 3 = 13.

✏️ Worked examples

1. f(g(2)) with f(x) = 2x + 3 and g(x) = x² + 1: g(2) = 5, then f(5) = 13.

2. g(f(2)), the same functions in the other order: f(2) = 7, then g(7) = 49 + 1 = 50.

⚠️ Watch out

• Order matters: f(g(2)) and g(f(2)) are usually different.

🎯 Try these

f(x) = 3x − 1 and g(x) = x² + 2.

1. f(g(1))
2. g(f(1))
3. f(g(3))

Answers: 1) 8 2) 6 3) 32

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