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4.1 Composite Functions

Composite Functions

  • A composite function is different from sum or product of functions; it is like a function acting on the result of another. If you picture functions as machines (with x as the input, and f(x) as the output), it is something like the diagram shown.

Note: Here, f(x)=3 x+2,\ g(x)=x^{2}, and x=3.

  • In comparison, (f+g)(x) is more like tow machines working separately with the same input x, and their two, separate outputs are placed together and packaged.
  • Just like how the processes of manufacturing has an order, so does composite functions. It is important which functions comes first, and which comes next. Using the example above where f is the first function), we write the composition of g with f (say we call it as h) as h=g \circ f (read as ‘composition of f followed by g‘). The rule of h(x) is given by
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