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3 cards from this section. Quick, good the night before a test.
Define function composition.
Think about how functions interact with each other.
What is required for composing functions?
Consider the sets involved.
What is the main requirement for two functions to be composed?
Think about how the functions are paired.
True or False: Function compositions can be commuted.
Consider what you learned about the order of operations.
Let f(x) = 2x, g(x) = x + 5, and h(x) = x^2. Compute h◦(f◦g)(x) and determine if the result matches (h◦f)◦g(x).
Calculate both sides step by step, evaluating at similar points.
Propose a different pair of functions, f and g, and demonstrate that f◦g is not equal to g◦f by providing specific values.
Choose different simple functions to illustrate this behavior.
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