Functions

A function f

A function f: A → B assigns exactly one element y in B to each element x in A. Key components include: Domain A (set of all inputs), Co-domain B (set

One

One-One (Injective): Different inputs give different outputs. Test: If f(a) = f(b), then a = b. Example: f(x) = 2x is one-one. Onto (Surjective): Ever

Function evaluation involves substituting values

Function evaluation involves substituting values: If f(x) = 3x² - 2x + 1, then f(2) = 3(4) - 2(2) + 1 = 9. For composite evaluation: f(g(x)) means sub

Constant Function

Constant Function: f(x) = k (horizontal line, range = {k}). Identity Function: f(x) = x (diagonal line, domain = range = R). Linear Function: f(x) = a

Composite function (g∘f)(x) = g(f(x)) means

Composite function (g∘f)(x) = g(f(x)) means apply f first, then g to the result. Example: If f(x) = x + 2 and g(x) = 3x, then (g∘f)(x) = g(x + 2) = 3(