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Question
Classify the following function as injection, surjection or bijection :
f : R → R, defined by f(x) = |x|
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Solution
f : R → R, defined by f(x) = |x|
Injection test:
Let x and y be any two elements in the domain (R), such that f(x) = f(y)
f(x) = f(y)
|x|=|y|
x=±y
So, f is not an injection .
Surjection test :
Let y be an element in the co-domain (R), such that f(x) = y for some element x in R (domain).
f(x) = y
|x|=y
x = ± y ∈ Z
So, f is a surjection and f is not a bijection.
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