Question

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

The correct option is A One-one but not onto

By graph, we can see that for three different value of $x$, we get unique value of $y.$

Hence $f\left(x\right)$ is not $one-one$.

But $f\left(x\right)$ is defined for each value of $x$.

Here $f\left(x\right)$ is $onto.$