Question

The function $f:R \rightarrow R$ defined by $f(x) = (x - 1)(x - 2)(x - 3)$ 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

Answer 2

We have $f(x) = (x - 1)(x - 2)(x - 3)$

$\Rightarrow f(1) = f(2) = f(3) = 0 \Rightarrow f(x)$ is not one-one

For each $y \in R,$ there exists $x \in R$ such that $f(x) = y$. Therefore f is onto.

Hence, $f:R \rightarrow R$ is onto but not one-one.