Composite Functions

This topic introduces learners to composite functions, where one function is applied to the result of another function. Students will understand how to combine functions and evaluate composite functions, exploring their domain and range. This foundational concept is essential in understanding complex functional relationships and prepares learners for advanced algebra and calculus topics.

Learning Outcomes:
The learner should be able to:

• understand and use function notation.
• describe and understand a composite function.
• Understand and apply the notation for composite functions (f ∘ g)(x).
• Evaluate composite functions for given inputs.
• Determine the domain and range of composite functions.
• work out the inverse of a function and recognise the graphical relationship between a function and its inverse.
• Solve problems involving composite functions in various contexts.
• Recognize real-life situations where composite functions are applied.