Chapter 1: Functions
FUNCTION NOTATION AND EVALUATION
Notation: f(x) means value of function f at x.
Example: If f(x) = 2x + 3, find f(5). Solution: f(5) = 2(5) + 3 = 13.
DOMAIN AND RANGE
Example: For f(x) = 1/(x-2), domain excludes x = 2.
COMPOSITE FUNCTIONS
If f(x) = x + 2 and g(x) = x^2, then (f ? g)(x) = f(g(x)) = (x^2) + 2.
INVERSE FUNCTIONS
Inverse reverses mapping. Example: If f(x) = 2x + 3, then f?¹(x) = (x - 3)/2. Horizontal Line Test: A
function has an inverse if it is one-to-one.
Visual Representations