Classify the function as injection, surjection or bijection f: N → N given by f(x) = x2

Asked by Sakshi | 1 year ago |  61

##### Solution :-

Given f: N → N, given by f(x) = x2

Now we have to check for the given function is injection, surjection and bijection condition.

Injection condition:

Let x and y be any two elements in the domain (N), such that f(x) = f(y).

f(x) = f(y)

x= y2

x = y (We do not get ± because x and y are in N that is natural numbers)

So, f is an injection.

Surjection condition:

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

x2= y

x = $$\sqrt{y}$$, which may not be in N.

For example, if y = 3,

x = $$\sqrt{3}$$ is not in N.

So, f is not a surjection.

Also f is not a bijection.

Answered by Aaryan | 1 year ago

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