Functions & inverse functions
AQA GCSE Maths revision on Functions & inverse functions. Aligned to the AQA GCSE Mathematics 8300 specification. This bank has 16 practice questions on this topic.
Sample questions (3 of 16)
-
Question 1
If a function f(x) maps an input to a unique output, what must be true for the inverse function f⁻¹(x) to exist?
- A) The function must be one-to-one
- B) The function must have a positive gradient
- C) The function must be a straight line
- D) The function must pass through the origin
Show answer
Answer: The function must be one-to-one
For a function to have an inverse, every output must correspond to exactly one input. If a function is many-to-one, like a parabola, the inverse would be one-to-many, which violates the definition of a function.
-
Question 2
A student claims that the inverse of f(x) = x - 5 is f⁻¹(x) = 5 - x. What is the fundamental error in this reasoning?
- A) They confused the inverse with the negative function
- B) They should have squared the x
- C) They forgot to change the sign of the constant
- D) They used the wrong variable
Show answer
Answer: They confused the inverse with the negative function
The inverse function reverses the operations applied to x. Subtracting 5 is undone by adding 5, whereas the student simply negated the entire expression, which does not reverse the mapping.
-
Question 3
What is the graphical relationship between a function y = f(x) and its inverse y = f⁻¹(x)?
- A) Reflection in the line y = x
- B) Rotation of 180 degrees about the origin
- C) Reflection in the x-axis
- D) Translation by the vector (1, 1)
Show answer
Answer: Reflection in the line y = x
Because an inverse function swaps the roles of inputs and outputs, every point (a, b) on the original graph becomes (b, a) on the inverse graph. This transformation is geometrically defined as a reflection across the line y = x.
Want to test yourself on the remaining cards for this topic?
13 more questions on Functions & inverse functions — plus mistakes tracking and spaced repetition across the whole Maths spec.