Functions

A function is a rule that gives exactly one output for each input. In this topic you will learn function notation, how to evaluate functions, find composite functions and inverse functions. We also look at domain and range for simple functions.

  • Function notation and evaluation
  • Composite functions
  • Inverse functions
  • Domain and range

Lessons for Functions

Function Notation and Evaluation

Notationf(x) = 2x + 3 means the function named f multiplies the input by 2 then adds 3.f: x → …

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Composite Functions

Composite functionfg(x) means f(g(x)). Do g first, then put that answer into f.Example: f(x) = 2x + 1, g(x) = …

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Inverse Functions

Inverse functionf-1(x) reverses the effect of f(x). If f(a) = b then f-1(b) = a.Method: Let y = f(x), swap …

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Domain and Range

DomainDomain = all possible input values x. Look for values that make the function undefined.Example: f(x) = 1/x. Domain: x …

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Exercises for Functions

Evaluate functions

Given f(x) = 3x - 2, g(x) = x2 + 1, h(x) = 4/x, find:f(4)g(-3)h(2)f(-1)g(0)h(-4)

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Find composite functions

Given f(x) = x + 4, g(x) = 3x, h(x) = x2:Find fg(x)Find gf(x)Find fh(x)Find hf(2)Find gg(x)

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Find inverse functions

Find f-1(x) for:f(x) = x + 7f(x) = 4xf(x) = 3x - 6f(x) = (x - 2)/5f(x) = 5 - …

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State domain and range

State the domain and range for:f(x) = 5x - 3f(x) = x2 + 2f(x) = 3/xf(x) = √(x - 1)f(x) …

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