Composite Function

Free interactive math game: Composite Function — f(g(x)). Part of the Functions category on MathKite.

Example problems

Taken from the generator that powers this exercise. A fresh set appears every time the page is opened, and the printable worksheet holds ten of them.

  1. f(x) = 3x + 5 g(x) = 3x + 1 f(g(5)) =
  2. f(x) = 3x g(x) = 2x + 5 f(g(5)) =
  3. f(x) = 4x − 1 g(x) = 3x + 1 f(g(3)) =
  4. f(x) = 4x + 1 g(x) = 3x f(g(2)) =

About this exercise

Applying one function to the result of another.

How to solve it

Work from the inside outwards: evaluate the inner function first, then feed its result into the outer one.

Worked example

With f(x) = x + 1 and g(x) = 2x, the value of f(g(3)) is f(6) = 7.

Common mistake

Applying them in the wrong order. The inner function is the one written closest to the input.