Cambridge O Level Additional Mathematics · Syllabus 4037 · Functions
Domain and Range
What is Domain and Range?
The domain of a function is the set of input values it is permitted to take; the range, also called the image set, is the set of output values that domain actually produces. Changing the domain changes the range, so a domain must be stated or deduced before any range can be found.
This definition is part of the Functions chapter in Cambridge O Level Additional Mathematics.
Questions students ask about Domain and Range
How do you show that a function and its inverse are reflections in \(y=x\)?
Reflecting a point in the line \(y=x\) swaps its coordinates, so the point \((a,b)\) on \(y=f(x)\) corresponds to \((b,a)\) on \(y=f^{-1}(x)\). In an exam, sketch \(y=f(x)\), draw the dashed line \(y=x\), and reflect the curve in it, making sure the domain and range have swapped over. Any point where the two graphs meet lies on the line \(y=x\) itself.