Function Composition and Operations

Given two functions f and g, you can create new functions: | Operation | Notation | Definition | |---|---|---| | Sum | (f + g)(x) | f(x) + g(x) | | Difference | (f - g)(x) | f(x) - g(x) | | Product | (f cdot g)(x) | f(x) cdot g(x) | | Quotient | left(frac{f}{g}right)(x) | frac{f(x)}{g(x)} (where g(x) neq 0) | These are straightforward — just apply both functions and combine.

Composition is plugging one function INTO another: [formula] Read it as: "f of g of x" — first apply g, then apply f to the result. Important: f(g(x)) neq g(f(x)) in general! Order matters.

Example: If f(x) = 2x + 3 and g(x) = x^2, find f(g(2)).