Question

Let $f:R\to R$ be defined as $f\left(x\right)=3x$. Choose the correct answer.

• A. $f$ is one-one onto
• B. $f$ is many-one onto
• C. $f$ is one-one but not onto
• D. $f$ is neither one-one nor onto

Answer 1

The correct option is A $f$ is one-one onto

$f:R\to R$ is defined as $f\left(x\right)=3x$.

Let $x,y\in R$ such that $f\left(x\right)=f\left(y\right)$

$\Rightarrow 3x=3y$
$\Rightarrow x=y$
$\therefore f$ is one-one
Also, for any real number $\left(y\right)$ in co-domian $R$,
there exists $\frac{y}{3}$ in $R$ such that
$f\left(\frac{y}{3}\right)=3\left(\frac{y}{3}\right)=y$

$\therefore f$ is onto.

Hence, function $f$ is one-one and onto
The correct answer is $A$.