Classify the following functions as injection, surjection or bije… - Vidyadip

Question

Classify the following functions as injection, surjection or bijection:
f : R → R, defined by f(x) = |x|

✓

Answer

f : R → R, given by f(x) = |x|
Injectivity: Let $\text{x, y}\in\text{R}$ such that
x = y but if y = -x
⇒ |x| = |y| ⇒ |y| = |-x| = x
$\therefore$ f is not one-one.
Surjective: Since f attains only positive values, for negative real numbers in R, there is no pre-image in domain R.
$\therefore$ f is not onto.

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 "3 Marks Question" from Functions→Functions — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Let $\text{A}=\begin{bmatrix}2&-3\\-7&5\end{bmatrix}$ and $\text{B}=\begin{bmatrix}1&0\\2&-4\end{bmatrix},$ verify that
$(\text{A}+\text{B})^\text{T}=\text{A}^\text{T}+\text{B}^\text{T}$

Evaluate the following integrals:
$\int\frac{\big\{\text{e}^{\sin^{-1}\text{x}}\big\}^2}{\sqrt{1-\text{x}^2}}\text{dx}$

Evaluate the following integrals:$\int\frac{1}{\sqrt{(1-\text{x}^2)\big\{9+\big(\sin^{-1}\text{x}\big)^2\big\}}}\text{ dx}.$

A random variable $X$ can take all non negative integral values and the probability that $X$ takes the value is proportional to $5^{-r}$. Find $P(X<3)$

Integrate the rational function $\frac{1}{x\left(x^{n}+1\right)} [$Hint: multiply numerator and denominator by $x^{n-1}$ and put $x^n = t]$

Manufacturer can sell x items at a price of rupees $(5-\frac{\text{x}}{100})$ each. The cost price is Rs $\Big(\frac{\text{x}}{5}+500\Big)$. Find the number of items he should sell to earn maximum profit.

Find the value of $\tan \frac{1}{2}\left[ {{{\sin }^{ - 1}}\frac{{2x}}{{1 + {x^2}}} + {{\cos }^{ - 1}}\frac{{1 - {y^2}}}{{1 + {y^2}}}} \right]$, |x| < 1, y > 0 and xy < 1

The amount of pollution content added in air in a city due to $x$ diesel vehicles is given by $P(x) = 0.005x^3 + 0.02x^2 + 30x.$ Find the marginal increase in pollution content when $3$ diesel vehicles are added and write which value is indicated in the above questions.

Find the position vector of the mid-point of the vector joining the points $\text{P}\big(2\hat{\text{i}}-3\hat{\text{j}}+4\hat{\text{k}}\big)$ and $\text{Q}\big(4\hat{\text{i}}+\hat{\text{j}}-2\hat{\text{k}}\big)$.

If the probability of a defective bolt is 0.1, find the (1) mean and (2) standard deviation for the distribution of bolts in a total of 400 bolts.