 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2019/discrete-mathematics-continuous-mathematics-and-probability-resit/1/b/iv/solution

Not injective; surjective. The equal values

f (0) = f (2) = 1

disprove injectivity. For any

y > 0

, take

x = 1 + y^{- 1/2} > 1

. This lies in the stated domain of a function, and

\frac{1}{( 1 - ∣ x ∣ ) ^{2}} = \frac{1}{( - y ^{- 1/2} ) ^{2}} = y .

Consequently every member of the codomain has a preimage.

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