Question

Check the injectivity and surjectivity of the following functions:
(i)f : N → N given by f(x) = x2

Answer 1

Answer:

injective but not surjective

Explanation:

f(x)=x ^2

 

It is seen that for x,y∈N,

f(x)=f(y)⇒x ^2 = Y^2  

⇒x=y

∴f is injective

Now, 2∈N, But, there does not exist any x

in N such that f(x)=x^2 = 2  

 

∴f is not surjective.

Hence, function f is injective but not surjective.