Inverse function

Definition

An inverse function reverses the effect of the original function. Graphically it is the reflection in the line y = x. A function only has an inverse that is also a function if it is one-to-one, which is why parabolas need a restricted domain.

Worked example

If f(x) = 3x − 1 then f⁻¹(x) = (x + 1)/3.

Where it appears in the exam

Paper 1 asks you to find the inverse of a linear, quadratic or exponential function, sketch it as a reflection in y = x, and restrict a parabola's domain so the inverse is a function.

Step-by-step method

1. Write the function as y = f(x).
2. Swap x and y.
3. Make y the subject.
4. Write f⁻¹(x) = … and state any domain restriction.

Common mistake

Not restricting the domain of y = ax² before finding the inverse, so the inverse is not a function.

Related functions terms

• Asymptote
• Domain and range

Frequently asked questions

What does inverse function mean in Grade 12 Maths?

An inverse function reverses the effect of the original function. Graphically it is the reflection in the line y = x. A function only has an inverse that is also a function if it is one-to-one, which is why parabolas need a restricted domain.

Which NSC paper tests inverse function?

Inverse function belongs to the Functions section of CAPS Grade 12 Mathematics, which is examined in Paper 1.

How do I practise questions involving inverse function?

Snap a question that uses inverse function into the Snap&Learn AI solver, or work through the functions topic guide and NSC past papers.