This IB Maths AI HL 2.7 resource introduces composite and inverse functions, including domain restrictions, and is fully aligned with the IB Applications and Interpretation HL syllabus.

Students begin by reviewing the idea that a function maps each input in its domain to exactly one output in its range. The notes then introduce composite functions as a process where the output of one function becomes the input of another, helping students understand notation such as f(g(x)) and g(f(x)).

The resource develops students’ understanding that the order of composition matters. Guided examples and practice problems show students how to substitute one function into another, simplify composite expressions, and compare results such as f(g(x)) and g(f(x)).

Inverse functions are then introduced as functions that reverse the inputs and outputs of the original function. Students learn why a function must be one-to-one in order to have an inverse, and how repeated outputs can prevent the inverse from being a function.

The notes also explain why domain restrictions are sometimes needed, using the square function as a key example. Students see how restricting the domain allows an inverse function to be defined, and how the graph of an inverse relates to the original function.

Structured practice guides students through formal inverse notation, the steps for finding an inverse algebraically, and checking inverse relationships using composition. The exit check gives students a chance to explain why composition order matters and why some functions require restricted domains before an inverse exists.

Ideal for IB Maths AI HL teachers teaching composite functions, inverse functions, function notation, one-to-one functions, domain restrictions, and algebraic methods for finding inverses.

This pairs great with our slidedeck!