Question

Function $f:N\to N,f\left(x\right)=2x+3$ is

• A. One-one Onto function
• B. One-one Into function
• C. Many-one Onto function
• D. Many-one Into function

Answer 1

The correct option is B One-one Into function

For any $x_1,x_2\in N$ with $x_1\ne x_2$
$2x_1+3\ne 2x_2+3$
$\therefore f\left(x_1\right)\ne f\left(x_2\right)$
Therefore, function is one-one.

Also $y=2x+3$
$\Rightarrow x=\frac{y-3}{2}$
$\therefore R_f=N-\{1,2,3,4\}$
Therefore, function is not onto.

Hence, the given function is One-one and Into.