Q. 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
Explanation
(b)
Given, $f(x) = (x - 1)(x - 2)(x - 3)$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ f(1) = f(2) = f(3) = 0$
$\Rightarrow \ f(x)$ is not one-one.
For each $y \in R$, there exists $x \in R$ such that $f(x) = y$.
Therefore, $f$ is onto.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.