Question

F(x)= x² - 2x+3 and g(x) = 2x+1 find the following
f(g(x))
Help please

Answer 1

f(g(x)) = 4x² + 2

General Formulas and Concepts:

Algebra I

• Compositions of Functions
• Function Notations
• Expanding by FOIL-ing
• Combining Like Terms

Explanation:

Step 1: Define

f(x) = x² - 2x = 3

g(x) = 2x + 1

Step 2: Find f(g(x))

1. Substitute in g(x) into f(x): f(g(x)) = (2x + 1)² - 2(2x + 1) + 3
2. Expand: f(g(x)) = 4x² + 4x + 1 - 2(2x + 1) + 3
3. Distribute -2: f(g(x)) = 4x² + 4x + 1 - 4x - 2 + 3
4. Combine like terms (x): f(g(x)) = 4x² + 1 - 2 + 3
5. Combine like terms (Z): f(g(x)) = 4x² + 2