Function Notation
f(x) is the output for input x. Substitute the input everywhere x appears.
The rules
- Replace every x with the input, using parentheses.
- f(a + 1) means substitute a + 1 for x.
- If f(x) = 3, find x by solving the equation.
- On a graph, f(2) is the y-value at x = 2.
Watch out: Forgetting parentheses when substituting a negative (f(−2) for x² gives 4, not −4).
Worked example
If f(x) = x² − 3x, what is f(−2)?
- (−2)² − 3(−2).
- 4 + 6 = 10.
Answer: 10
Try it yourself
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