What is a composite function?

• A?composite function?is where one function is applied after another function

• The ‘output’?of one function will be the ‘input’?of the next one
• Sometimes called?function-of-a-function
• A composite function can be denoted
  • 
  • 
  • 
  • 
  • All of these mean “ ”

How do I work with composite functions?

• Recognise?the notation
  • fg(x)?means?“f?of?g?of?x”

  The order matters

  • First apply?g?to?x?to get
  • Then apply?f to the previous output to get
  • Always start with the function?closest to the variable
  • is not usually equal to

Special cases

• fg(x)?and?gf(x)?are generally different but can sometimes be the same
• ff(x)?is written as?f2(x)
• Inverse functions?ff-1(x) = f-1f(x) = x