Mathematics · Grades 9–12
Compose two functions
Apply the inside function first.
The key idea
Apply the inside function first.
(f ∘ g)(x) = f(g(x))
Worked examples
f(t) = 4t + (-3); g(t) = 5t + (-5). Find f(g(7)).
g(7) = 30; f(30) = 117
117
f(t) = 4t + (10); g(t) = 4t + (-6). Find f(g(5)).
g(5) = 14; f(14) = 66
66
Try it yourself
f(t) = 5t + (6); g(t) = 1t + (-2). Find f(g(4)).
f(t) = 3t + (-10); g(t) = 3t + (-4). Find f(g(3)).
Check your understanding
Answers and marking notes
- 16
g(4) = 2; f(2) = 16
- 5
g(3) = 5; f(5) = 5
Further reading and review references
These are reference links, not copied exercises, institutional endorsement or proof of independent review.
Learning preview · teacher review required. Grade bands are approximate, not official curriculum alignment.