Question

$A=\left\{\begin{array}{c}1,2,3,4\end{array}\right\},B=\left\{\begin{array}{c}1,2,3,4,5,6\end{array}\right\}$ are two sets, and function $f:A\to B$ is defined by $f\left(x\right)=x+2\forall x\in A$, then the function f is

• A. Bijective
• B. Onto
• C. One-one
• D. Many-one

Answer 1

Answer: (C)

One-one

Given, $A=\left\{\begin{array}{c}1,2,3,4\end{array}\right\}$
and $B=\left\{\begin{array}{c}1,2,3,4,5,6\end{array}\right\}$
Let $f\left(x\right)=f\left(y\right)$
$\Rightarrow x+2=y+2[\because f(x)=x+2]$
$\Rightarrow x=y$
Hence, $f$ is one-one.