IGCSE Additional Mathematics (0606)

Domain and range

What this topic tests, the mistakes that cost marks, and one exam-style question worked through step by step.

Key ideas and common mistakes

A quadratic function is one-one only if its domain is restricted to one side of its vertex (the axis of symmetry).
Common mistake: The trap is choosing a value of a that allows both sides, making the function not one-one.
The range of an inverse function is the domain of the original function.
Common mistake: Students must correctly identify and transfer the domain restriction from the original to the inverse, not confuse it with the original range.
For a quadratic function restricted to x-values at or beyond its vertex, the range starts at the minimum (or maximum) value at the vertex, not at the x-coordinate of the vertex or the unrestricted range.

Find the least possible value of a.

Try it first, then show the working

Complete the square: f(x) = (x - 3)^2 - 8, so the curve has its vertex at x = 3.
f is one-one only on a domain that does not straddle the vertex, so the least value is a = 3.

Answer: a = 3

11 exam-style questions on Domain and range, each marked to the scheme.