Advanced · 15 min
Functions and composition
Treat a function as an input-output rule and apply two rules in order.
Evaluate a function
The notation f(x) names a function's output for input x; it does not mean f multiplied by x. Substitute the input into the whole rule.
Worked example
If f(x) = x² + 1, then f(3) = 10.
Compose in the stated order
In f(g(x)), evaluate g first and use its output as the input to f. Reversing the order can change the result.
Worked example
If f(x) = x + 2 and g(x) = 3x, then f(g(4)) = 14, while g(f(4)) = 18.
Compare compositions
- Use f(x) = x − 1 and g(x) = x² to find f(g(3)).
- Calculate g(f(3)) and explain why the order matters.