Past exam of the year 1 of the computer science course of the University of Oxford / 2023 / Discrete mathematics, probability and continuous mathematics / 2 / d / i

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- Solution i

Solution

Suppose

(g \circ f) (a) = (g \circ f) (a^{'})

. Injectivity of

g

gives

f (a) = f (a^{'})

, and injectivity of

f

then gives

a = a^{'}

. Thus the function composition is injective.

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