Relations and Functions — Class 12 Maths Solution

Option A is correct

Injectivity

Let ${x_1},\;{x_2} \in R$ such that $f({x_1}) = f({x_2}),$
$\Rightarrow$ $3{x_1} = 3{x_2} \Rightarrow {x_1} = {x_2} \Rightarrow f$ is one-one.

Surjectivity

For any $y \in R$ (co-domain of f), there exist $x \in R$ (domain of f) such that
$f(x) = y \Rightarrow 3x = y \Rightarrow x = \cfrac{y}{3}$

$\Rightarrow$ $f(x) = f\left( {\cfrac{y}{3}} \right) = 3.\cfrac{y}{3} = y$
$\Rightarrow$ f is onto
Thus, f is one-one and onto.