Concept:A composite function is classified by whether it has distinct outputs for distinct inputs (one-to-one) or covers all elements of its codomain (onto).
Explanation:From the given arrow diagram,
y=g(x) is one-to-one; each input
x leads to a different
y.
Next,
z=h(y) is not one-to-one because some different
y-values give the same
z.
However,
h is onto, so every element in the final set is the image of at least one
y.
Looking at the combined composite, the repetition in
h prevents the composite from being one-to-one.
The composite arrows still cover every element of the final set, so no element in the codomain is missed.
This means the composite function is onto, not merely a relation or a series.
Answer:B. onto
