The function f:R R defined by f(x) = (x - 1) (x - 2)(x - 3) is - Vidyadip

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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