Functions & Inverses
Function Notation
Function notation names a rule and shows its input. The expression f(x) means the output of f when the input is x.
What f(x) means
f is the name of the function and x is the input. Writing f(x) = 2x + 1 describes the whole rule. It does not mean “f times x.”
How to read function notation
- Identify the function name, such as f or g.
- Identify the input inside the parentheses.
- Read f(x) as “the output of f for input x.”
- Remember that different letters can name different functions.
Worked example
Read f(x) = 3x − 2
- The function is named f.
- The input is x.
- The output is 3x − 2.
f(x) means the output of f when the input is x.
Common mistakes
- Reading f(x) as multiplication.
- Thinking the letter inside the parentheses must always be x.
- Confusing the function name with the input value.
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