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Question
Classify the following function as injection, surjection or bijection : f : N → N given by f(x) = x3
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Solution
f : N → N, given by f(x) = x3
njection test :
Let x and y be any two elements in the domain (N), such that f(x) = f(y).
f(x) = f(y)
x3 = y3
x = y
So, f is an injection
Surjection test :
Let y be any element in the co-domain (N), such that f(x) = y for some element x in N (domain).
f(x) = y
x3= y
x=`3sqrty ` which may not be in N.
For example, if y = 3,
x= `3sqrt3` is not in N .
So, f is not a surjection and f is not a bijection.
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