For f(x) = x + 4 and g(x) = 3x, find f(g(2)).
Incorrect answer: 18
Function composition is not multiplication. f(g(x)) applies one rule after another; f(x)g(x) multiplies two separate outputs.
Applying functions in the wrong order
Read composition from the inside out. Evaluate the inner output before applying the outer rule.
The correction
10
g(2) = 6, then f(6) = 10.
- Read from the inside outward to identify which function acts first.
- Substitute the entire inner expression for each input in the outer function.
- Check that the inner input is allowed and its output lies in the outer function’s domain.
Try the reasoning in another example
For the same functions, find g(f(3)).
- First f(3) = 7.
- Then g(7) = 7².
Answer: 49
Explain why each step preserves the quantity or relationship. If you can compute the answer but cannot explain the step, revisit the model before adding more questions.
The short check below reuses the first example as a retrieval question and adds a second question. It checks this method; it does not establish a grade level.
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