Question

The function $f:R\to R$ defined as $f\left(x\right)=(x-1)(x-2)(x-3)$ is

• A. One-one but not onto
• B. Onto but not one-one
• C. Both one-one and onto
• D. Neither one-one nor onto

Answer 1

Answer: (B)

Onto but not one-one

Given, $f\left(x\right)=(x-1)(x-2)(x-3)$
and $f\left(1\right)=f\left(2\right)=f\left(3\right)=0$
$\Rightarrow f\left(x\right)$ is not one-one.
For each $y\in R$, there exists $x\in R$, such that $f\left(x\right)=y$.
Therefore, $f$ is onto. Hence, $f:R\to R$ is onto but non one-one.