 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2016/discrete-mathematics-continuous-mathematics-and-probability/3/e/iii/solution

Take

f (n) = g (n) = n^{2}

, so

h (n) = n^{2}

but

(f \circ g) (n) = n^{4}

(f \circ g) (n) / h (n) = n^{2}

is unbounded, precluding any eventual constant upper bound in big O notation. False: in general $f \circ g \neq = O (h)$ . This is a counterexample involving function composition, not pointwise addition.

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