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 f(x) is a shorthand that names a function (f) and specifies its input (x). Writing f(3) = 10 means that when the input is 3, the function produces the output 10. This notation is not multiplication.

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

easy
If f(x) = 3x^2 - 2x + 1, find f(-2).

Example 2

medium
If g(x) = x^2 + 3x, find and simplify \frac{g(x+h) - g(x)}{h}.

Example 3

medium
If f(x) = 2x - 1 and g(x) = x^2 + 3, find (f \circ g)(x) and (g \circ f)(x).

Example 4

hard
A function satisfies f(x+1) = 2f(x) + 3 for all x, with f(0) = 1. Find f(1), f(2), and f(3).
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