Question

$A=\left\{1,2,3,4\right\}$ and $B=\left\{1,2,3,4,5,6\right\}$ are two sets and function $f:A\to B$ is defined by$f\left(x\right)=x+2,$ for all $x$ belongs to $A$, then the function $f$ is.

• A. bijective
• B. one
• C. one-one
• D. many-one

Answer 1

The correct option is C

one-one

Explanation for correct answer:

Applying the condition of one-one function:

In mathematics, a function from a set $X$to a set $Y$ assigns to each element of $X$ exactly one element of $Y$ . The set $X$ is called the domain of the function and the set $Y$ is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity.

We have the following $A=\left\{1,2,3,4\right\}$ and $B=\left\{1,2,3,4,5,6\right\}$

$f\left(x\right)=x+2$

$$\begin{gathered} Atx=1,f\left(x\right)=3 \\ Atx=2,f\left(x\right)=4 \\ Atx=3,f\left(x\right)=5 \\ Atx=4,f\left(x\right)=6 \end{gathered}$$

Hence f (x) is one-one but codomain ≠ range.

Hence, option(C) is correct.