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

Answer: (B)

Let $x_1$ and $x_2$ be any two elements of $N$.
$\therefore f\left(x_1\right)=f\left(x_2\right)$
$\Rightarrow 2x_1+3=2x_2+3$
$\Rightarrow x_1=x_2$
$\therefore f$ is one-one function.
Now, let $y=2x+3\Rightarrow x=\frac{y-3}{2}$
It is not onto function, because for $y=3,x=0\notin N$.
Hence, it is one-one into function.