For f(x) = 5x − 2, find f(3).
Incorrect answer: 15
f(4) asks for an output at input 4; solving f(x) = 4 asks which inputs produce output 4. Also, (−3)² is 9, whereas −3² means −9.
Treating function notation as multiplication
f(3) asks for the output at input 3. It does not mean f times 3; negative inputs also need parentheses.
The correction
13
5(3) − 2 = 15 − 2 = 13.
- Identify the input inside the parentheses.
- Substitute that input everywhere the variable occurs, using parentheses for negative numbers or expressions.
- Calculate in order and check any domain restrictions, such as a denominator that cannot be zero.
Try the reasoning in another example
For g(x) = x² − 1, find g(−3).
- Use parentheses: (−3)² − 1.
- The square is 9; subtract 1.
Answer: 8
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