Mathematics for IGCSE & O level - Functions (Section 2 - No. 7)
Which of the following are key concepts when working with composite functions?
g(f(x)) means applying f first, then applying g.
The range of f(x) becomes the domain for g(x) when determining g(f(x)).
g(f(x)) and f(g(x)) will always result in the same expression.
Composite functions are only defined if both functions are linear
Explanation
g(f(x)) means applying f first, then applying g, and the range of f(x) impacts the domain of g(x). f(g(x)) and g(f(x)) are usually different. Composite functions are not limited to linear functions.