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.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from 1. relation and function→1. relation and function — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Let $f (x + y) = f (x) + f (y)$ for all $x , y \in R.$ Then :

If the ordinate $x = a$ divides the area bounded by the curve $y = \left( {1 + \frac{8}{{{x^2}}}} \right)\,,$ $x - $ axis and the ordinates $x = 2,$ $x = 4$ into two equal parts, then $a = $

If $f(x)=\frac{\left(\tan 1^{\circ}\right) x+\log _{\varepsilon}(123)}{x \log _{\varepsilon}(1234)-\left(\tan 1^{\circ}\right)}, x > 0$, then the least value of $f(f(x))+f\left(f\left(\frac{4}{x}\right)\right)$ is $...........$.

The solution of $(x - {y^3})dx + 3x{y^2}dy = 0$ is

Let $a =$$\mathop {Lim}\limits_{x \to 1} \,\,\frac{x}{{\ln \,x}}\; - \;\frac{1}{{x\,\ln \,x}}$ ; $b =$$\mathop {Lim}\limits_{x \to 0} \,\,\frac{{{x^3} - 16x}}{{4x + {x^2}}}$ ; $c =$$\mathop {Lim}\limits_{x \to 0} \,\,\frac{{\ln (1 + \sin x)}}{x}$ and $d =$$\mathop {Lim}\limits_{x \to - 1} \,\,\frac{{{{(x + 1)}^3}}}{{3\left( {\sin (x + 1) - (x + 1)} \right)}}$ , then the matrix $\left[ {\begin{array}{*{20}{c}}a&b\\c&d\end{array}} \right]$ is

If the events A and B are independent, then $\text{P}(\text{A}\cap\text{B})$ is equal to,

P(A) + P(B)
P(A) - P(B)
P(A) P(B)
$\frac{\text{P(A)}}{\text{P(B)}}$

A coin is biased so that the head is $3$ times as likely to occur as tail. This coin is tossed until a head or three tails occur. If $X$ denotes the number of tosses of the coin, then the mean of $X$ is

The differential coefficient of $\text{f}(\log\text{x})$ w.r.t. x, where $\text{f(x)}=\log\text{x}$ is:

$\frac{\text{x}}{\log\text{x}}$
$\frac{\log\text{x}}{\text{x}}$
$(\text{x}\log\text{x})^{-1}$
$\text{None of these.}$

Find the inverse of each of the matrices (if it exists). $\left[\begin{array}{cc}-1 & 5 \\ -3 & 2\end{array}\right]$

The value of $(\hat{i} \times \hat{j}) \cdot \hat{j}+(\hat{j} \times \hat{i}) \cdot \hat{k}$ is: