42 self-marking GCSE and IGCSE practice questions on Inverse functions, written specifically for AQA, Pearson, OCR, Pearson International GCSE Maths A (4MA1), Cambridge IGCSE Mathematics (0580), Cambridge IGCSE (9-1) Mathematics (0980) across Higher and Extended tier. Instant marking with full worked solutions on every question.
A few of the 42 questions, from easier to harder. Choose your exam board and tier to practise them, with every answer marked.
Question 12 marksGrade 6-7
f(x)=7x−12
Find f−1(x)
What are the common mistakes in Inverse functions?
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.
Doesn't attempt to find the inverse operation/function when required
Wrote the original function back down instead of rearranging for the inverse
Undoes the operations in the wrong order when finding an inverse function
Divided by 4 first, then applied - 5 to the whole expression, instead of undoing the subtraction before dividing
Mishandles a sign when finding an inverse function involving a reciprocal
Kept the same sign as the original (x - 1) instead of flipping it when rearranging - the subtracted/added constant moves outside the fraction with its sign reversed.
Quick answers about Inverse functions
How many Inverse functions practice questions are there?
There are 42 self-marking GCSE and IGCSE Maths questions on Inverse functions, written for AQA, Pearson, OCR, Pearson International GCSE Maths A (4MA1), Cambridge IGCSE Mathematics (0580), Cambridge IGCSE (9-1) Mathematics (0980) across Higher and Extended tier. Each one is marked instantly and has a full worked solution.
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No. You can start practising Inverse functions straight away without an account. A free account keeps your results across sessions, so you can see your progress on this topic over time.
. Show your working.
Show the worked solution
Let y=7x−12
Add 12 to both sides: y+12=7x
Divide both sides by 7: x=7y+12M1
Swap x and y: f−1(x)=7x+12
Question 24 marksGrade 6-7
f(x)=4x+9
a) Work out f(2).
b) Find f−1(x). Show your working.
Show the worked solution
a) Substitute x=2 into f(x)=4x+9: f(2)=4(2)+9=17
Question 33 marksGrade 8-9
f(x)=x−24, x=2
Find f−1(x). Show your working.
Question 43 marksGrade 8-9
g(x)=3x+7
Solve g−1(x)=2x
Question 54 marksGrade 8-9
f(x)=4x+3
Show that f(x)−16f−1(x) simplifies to an integer, and find its value.
Question 65 marksGrade 8
The functions f and g are such that f(x) = 5x+3 and g(x) = ax+b, where a and b are constants.
g(3) = 20 and f⁻¹(33) = g(1).
Find the value of a and the value of b.