Answer:
f(g(x)) = 4x² + 2
General Formulas and Concepts:
Algebra I
- Compositions of Functions
- Function Notations
- Expanding by FOIL-ing
- Combining Like Terms
Step-by-step explanation:
Step 1: Define
f(x) = x² - 2x = 3
g(x) = 2x + 1
Step 2: Find f(g(x))
- Substitute in g(x) into f(x): f(g(x)) = (2x + 1)² - 2(2x + 1) + 3
- Expand: f(g(x)) = 4x² + 4x + 1 - 2(2x + 1) + 3
- Distribute -2: f(g(x)) = 4x² + 4x + 1 - 4x - 2 + 3
- Combine like terms (x): f(g(x)) = 4x² + 1 - 2 + 3
- Combine like terms (Z): f(g(x)) = 4x² + 2
