Classify the following functions as injection, surjection or bije… - Vidyadip

Question

Classify the following functions as injection, surjection or bijection:
f : Z → Z, defined by f(x) = x - 5

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Answer

f : Z → Z, defined by f(x) = x - 5Injection test: Let x and y be any two elements in the domain (Z), such that f(x) = f(y).
f(x) = f(y) x - 5 = y - 5 x = y Therefore, f is an injection. Surjection test: Let y be any element in the co domain (Z), such that f(x) = y for some element x in Z (domain). f(x) = y x - 5 = y x = y + 5, which is in Z. Therefore, f is a surjection and f is a bijection.

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