Practice Function Notation in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Function notation writes outputs as f(x) to show a rule assigning each input to an output.
The notation f(x) is not "f times x" — it means "the output of function f when the input is x." The parentheses contain the input, not a multiplication.
Example 1
easyIf f(x) = 3x^2 - 2x + 1, find f(-2).
Example 2
mediumIf g(x) = x^2 + 3x, find and simplify \frac{g(x+h) - g(x)}{h}.
Example 3
mediumIf f(x) = 2x - 1 and g(x) = x^2 + 3, find (f \circ g)(x) and (g \circ f)(x).
Example 4
hardA function satisfies f(x+1) = 2f(x) + 3 for all x, with f(0) = 1. Find f(1), f(2), and f(3).