Question

If three functions are composable, which associative property holds?

Options

• \(h\circ(g\circ f)=(h\circ g)\circ f\)

• \(h\circ(g\circ f)=h\circ(g+f)\)

• \(h\circ(g\circ f)=h+g+f\)

• \(h\circ(g\circ f)=f\circ(g\circ h)\)

Answer 1

Composition is associative whenever the functions are composable. The grouping of the compositions may change, but the order \(f\), then \(g\), then \(h\) remains unchanged.