Question

State whether the function f: N N given by
f(x) = 5x is injective, surjective or both.

Please help me !​

Answer 1

Answer:

Injectivity: f(X1)=f(X2)

5x1 = 5x2

i.e., X1 =X2

therefore function is one one(injective)

Surjectivity: Let y = f(x)

i.e., y =5x

x = y/5

[for y=1, x does not belong to N]

therefore, function is not onto(surjective)