Smart Math guide · Advanced Math Ideas

Think of Function Composition as a Pipeline

In f(g(x)), the output of g becomes the input of f.

All levelsWorked example includedSelf-check included
The method

How to use it

  1. Evaluate the inner function first.
  2. Substitute that result into the outer function.
  3. Track domain restrictions.
Worked example

See it in action

f(x)=x+1, g(x)=2x: f(g(3))=f(6)=7.

Check your thinking

How to verify it

Direct formula f(g(x))=2x+1 gives 7 at x=3.