Composite functions
AQA GCSE Maths revision on Composite functions. Aligned to the AQA GCSE Mathematics 8300 specification. This bank has 16 practice questions on this topic.
Sample questions (3 of 16)
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Question 1
If f(x) = x + 2 and g(x) = x^2, why is the composite function fg(x) different from gf(x)?
- A) Because addition is commutative but squaring is not.
- B) Because the order of operations changes which function is applied to the input first.
- C) Because composite functions are always equal to each other regardless of order.
- D) Because x represents a different value in each function.
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Answer: Because the order of operations changes which function is applied to the input first.
In fg(x), you apply g first, then f. In gf(x), you apply f first, then g. Since functions transform inputs differently, changing the sequence of these transformations generally results in a different final output.
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Question 2
A student calculates fg(x) by multiplying f(x) and g(x). What is the name of the error they have made?
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Answer: Confusion with algebraic multiplication
Multiplication of functions is denoted as (f * g)(x), which involves multiplying the two expressions. Composite functions, denoted as fg(x) or f(g(x)), involve substituting the entire expression of one function into the variable of the other.
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Question 3
Which statement correctly describes the domain of a composite function fg(x)?
- A) It is always the same as the domain of f(x).
- B) It is always the same as the domain of g(x).
- C) It is restricted to values of x for which g(x) is in the domain of f.
- D) It includes all real numbers regardless of the functions used.
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Answer: It is restricted to values of x for which g(x) is in the domain of f.
For fg(x), x must first produce a valid output from g(x). That output must then be a valid input for f(x). If g(x) produces a value outside the domain of f, that x-value cannot be part of the composite function's domain.
Want to test yourself on the remaining cards for this topic?
13 more questions on Composite functions — plus mistakes tracking and spaced repetition across the whole Maths spec.