Question

Let $f$ be a function from the set of natural numbers to the set of even natural numbers given by $f\left(x\right)=2x$. Then $f$ is

• A. One to one but not onto
• B. Onto but not one-one
• C. Both one-one and onto
• D. Neither one-one nor onto

Answer 1

Answer: (C)

Both one-one and onto

Now, for $x_1,x_2$ let $f\left(x_1\right)=f\left(x_2\right)$ then $2x_1=2x_2\Rightarrow x_1=x_2$.

So the given function is one-one.

Here range will be $2,4,6,8,\mathrm{10....}$ i.e every even natural number.

So $range=co-domain$.

Thus, the given function is onto.

Hence, C is correct.