9 self-marking Additional Maths practice questions on Composite functions (Additional Maths), written specifically for Cambridge IGCSE Additional Maths (0606) across Single tier. Instant marking with full worked solutions on every question.
A few of the 9 questions, from easier to harder. Choose your exam board and tier to practise them, with every answer marked.
Question 14 marksGrade 6
The functions f and g are defined for x∈R by
f(x)=−3x−8
What are the common mistakes in Composite functions (Additional Maths)?
When a pupil makes one of these on Revision Workshop, the marking engine names the mistake and explains it, instead of just marking the answer wrong.
Ignores the second function g when forming a composite function equation
Solved f(x) = 21 directly instead of fg(x) = 21, ignoring that g needs to be applied first.
Applies the two functions in a composite function in the wrong order
Swapped the order of application for part a) - worked out gf(3) instead of fg(3)
Applies the two functions in the wrong order for an algebraic composite function
Worked out gf(x) (substituted f into g) instead of fg(x) (substitute g into f) - the order in fg means apply g first.
Quick answers about Composite functions (Additional Maths)
How many Composite functions (Additional Maths) practice questions are there?
There are 9 self-marking Additional Maths Maths questions on Composite functions (Additional Maths), written for Cambridge IGCSE Additional Maths (0606) across Single tier. Each one is marked instantly and has a full worked solution.
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g(x)=4x−7
(a) Work out
fg(3)
. [2]
(b) Work out
gf(3)
. [2]
Show the worked solution
a) fg(3) means apply g first, then f.
g(3)=4(3)−7=5M1
f(5)=−3(5)−8=−23A1
b) gf(3) means apply f first, then g.
f(3)=−3(3)−8=−17M2
g(−17)=4(−17)−7=−75A2
Question 22 marksGrade 8
Consider the functions f(x)=ex and g(x)=x2−4x, both defined for x∈R.
Find fg(x), simplifying your answer. [2]
Show the worked solution
fg(x)=f(g(x))=f(x2−4x)=ex2−4x
Question 34 marksGrade 8
For all values of x, f(x) = (x+1)² and g(x) = 2(x−1).
(a) Show that gf(x) = 2x(x+2). [2]
(b) Find g⁻¹(7). [2]