MCQ
The function $f:R \to R$ defined by $f(x) = (x - 1)$ $(x - 2)(x - 3)$ is
  • A
    One-one but not onto
  • Onto but not one-one
  • C
    Both one-one and onto
  • D
    Neither one-one nor onto

Answer

Correct option: B.
Onto but not one-one
b
(b) We have $f(x) = (x - 1)(x - 2)(x - 3)$

$f(1) = f(2) = f(3) = 0$ ==> $f(x)$ is not one-one.

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

Therefore $f$ is onto. Hence $f:R \to R$ is onto but not one-one.

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