Mathematics·Functions and graphs · NSSCO 7.1

Functions & function notation

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A function is one of the most useful ideas in mathematics, and it is much friendlier than it sounds. In this lesson we picture a function as a little machine that takes a number in and sends a number out, then learn the special way we write it — function notation, f(x). We evaluate functions by substituting, solve f(x) = k by working backwards, join two machines together to make a composite function fg(x), and finally reverse a machine to find its inverse f⁻¹(x). We finish with a first look at domain and range.

What you'll learn in this lesson

By the end you should be able to (NSSCO Mathematics 7.1):

  • Describe a function as a rule (a mapping or machine) where each input gives exactly one output
  • Understand the terms function, one-one function, composite function and inverse function
  • Use function notation f(x) = 2x + 3 and the mapping form f : x → 2x + 3, with f⁻¹ for the inverse
  • Evaluate a function by substituting a value, e.g. find f(a)
  • Solve equations of the form f(x) = k to find the input
  • Form the composite of two functions, fg(x) = f(g(x)), and know that order matters
  • Find the inverse of a one-one function by swapping and solving
  • Understand the idea of the domain and range of a function
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Functions & function notation · NSSCO Mathematics · namstudy