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Functions

Functions​

Basics:

f(x) = rule that maps input x to output
Domain = allowed inputs
Range = possible outputs
Composite: (f o g)(x) = f(g(x))
Inverse: f^-1(x) reverses f(x)

Function types:

Even: f(-x) = f(x)
Odd: f(-x) = -f(x)
One-one: different inputs give different outputs
Onto: every output in codomain is hit

Speed checks:

  • Denominator cannot be zero.
  • Even root input must be non-negative.
  • Log input must be positive.
  • For inverse, swap x and y, then solve for y.