Functions & Inverses
Evaluating Functions
Evaluating a function means finding the output for a chosen input. Replace every copy of the input variable with the given number, then simplify.
Substitution into f(x)
If f(x) = 2x + 3, then f(4) means replace x with 4: 2(4) + 3 = 11. The same process works for any input, including zero and negatives.
How to evaluate a function
- Write the formula for f(x).
- Replace every x with the given input.
- Use parentheses for negative inputs.
- Simplify carefully.
- State the output value.
Worked example
Evaluate f(4) for f(x) = 2x + 3
- Start with f(x) = 2x + 3.
- Substitute: f(4) = 2(4) + 3.
- Simplify: 8 + 3 = 11.
f(4) = 11.
Common mistakes
- Substituting into only one occurrence of x.
- Dropping parentheses around a negative input.
- Treating f(4) as multiplication of f and 4.
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