📝 Chapter 8: Combining Functions

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8.1 — Sums and Differences
Question 1
If \( f(x) = x^2 \) and \( g(x) = 2x+1 \), then \( (f+g)(x) = \)
Solution:
\( (f+g)(x) = f(x) + g(x) = x^2 + (2x+1) = x^2 + 2x + 1 \)
8.3 — Composite Functions
Question 2
If \( f(x) = 2x-1 \) and \( g(x) = x^2 \), then \( f(g(x)) = \)
Solution:
\( f(g(x)) = f(x^2) = 2(x^2) - 1 = 2x^2 - 1 \)
Question 3
Using the same \( f \) and \( g \), \( g(f(x)) = \)
Solution:
\( g(f(x)) = g(2x-1) = (2x-1)^2 = 4x^2 - 4x + 1 \)
Note: \( f(g(x)) \neq g(f(x)) \) — composition is not commutative.