Question

Prove that the function f:N N defined by f(x) =2x is one to one but not onto​

Answer 1

Answer:

Step-by-step explanation:

Since we have given that

f: N to N is defined by

For one- one, let x₁, x₂ ε N

So, Let f(x₁) = f(x₂)

So, it is one-one.

Now, let y = 2x-1

So, we get that

But if we let y = 2

then,

And we know that 1.5 does not belong to natural numbers.

Hence, it is one-one but not onto.