Composition
Evaluate and simplify composite functions f(g(x)).
Objective
Evaluate and simplify composite functions f(g(x)).
What it means
Composition combines two functions so the output of one becomes the input of the other. (f ∘ g)(x) = f(g(x)) means you evaluate g first, then plug that result into f.
See it
Use this model while you read. Move it around to see what the math is doing.
3->2n + 1->7
Every input gets the same rule applied, so it gives exactly one output.
Key terms
- Composite function
- f(g(x)), read 'f of g of x'
- Inner function
- The function evaluated first, g(x)
- Outer function
- The function applied second, f(...)
Rules to remember
- Always evaluate the inner function first.
- Substitute the entire inner result into every x of the outer function.
- f(g(x)) is generally not equal to g(f(x)).
Step by step
- 1Identify inner and outerIn f(g(x)), g is inner, f is outer.
- 2Evaluate innerCompute g(x) or g(value).
- 3Plug into outerSubstitute the result into f.
Common mistakes
- Evaluating the outer function first.
- Mixing up f(g(x)) with g(f(x)).
Tips
- Work from the inside out.
- Write out the inner result before substituting.