Question:
The set of zeros of $ f(x) = 0 $ is a non-empty set, when $ f(x) = 0 $ , when $ f(x) $ is equal to
The set of zeros of $ f(x) = 0 $ is a non-empty set, when $ f(x) = 0 $ , when $ f(x) $ is equal to
Updated On: Mar 20, 2024
- $ e^{-x} + x $
- $ |x| + (x-2)^2 $
- $ x - log_e x $
- $ x + e^x $
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Answer (b) $ |x| + (x-2)^2 $
Was this answer helpful?
0
1
Top Questions on Relations and functions
- Let \[ L_1 : \frac{x-1}{1} = \frac{y-2}{-1} = \frac{z-1}{-1} \quad {and} \quad L_2 : \frac{x+1}{1} = \frac{y-2}{2} = \frac{z-2}{2} \] be two lines. Let \( L_3 \) be a line passing through the point \( (\alpha, \beta, \gamma) \) and be perpendicular to both \( L_1 \) and \( L_2 \). If \( L_3 \) intersects \( L_1 \) where \( 5x - 11y - 8z = 1 \), then \( 5x - 11y - 8z \) equals:
- JEE Main - 2025
- Mathematics
- Relations and functions
- Let the position vectors of three vertices of a triangle be \( \overrightarrow{p} = 4\hat{i} + \hat{j} - 3\hat{k} \), \( \overrightarrow{q} = -5\hat{i} + 2\hat{j} + 3\hat{k} \), and \( \overrightarrow{r} = -5\hat{i} + 3\hat{j} + 2\hat{k} \). Then \( \alpha + 2\beta + 5\gamma \) is equal to:
- JEE Main - 2025
- Mathematics
- Relations and functions
- Let the range of the function \[ f(x) = 6 + 16 \cos x \cdot \cos\left(\frac{\pi}{3} - x\right) \cdot \cos\left(\frac{\pi}{3} + x\right) \cdot \sin 3x \cdot \cos 6x, \quad x \in R \text{ be } [\alpha, \beta]. \] Then the distance of the point \((\alpha, \beta)\) from the line \(3x + 4y + 12 = 0\) is:
- JEE Main - 2025
- Mathematics
- Relations and functions
- The relation \( R = \{(x, y) : x, y \in \mathbb{Z} \text{ and } x + y \text{ is even} \} \) is:
- JEE Main - 2025
- Mathematics
- Relations and functions
- Let the position vectors of three vertices of a triangle be \( \overrightarrow{p} = 4\hat{i} + \hat{j} - 3\hat{k} \), \( \overrightarrow{q} = -5\hat{i} + 2\hat{j} + 3\hat{k} \), and \( \overrightarrow{r} = -5\hat{i} + 3\hat{j} + 2\hat{k} \). Then \( \alpha + 2\beta + 5\gamma \) is equal to:
- JEE Main - 2025
- Mathematics
- Relations and functions
View More Questions
Questions Asked in AMUEEE exam
- The ratio of the half-life time $ (t_{1/2}) $ , to the three quarter life-time, $ (t_{3/4}) $ , for a reaction that is second order
- AMUEEE - 2018
- Order of Reaction
- $ 0.002\, M $ solution of a weak acid has an equivalent conductance $ (\wedge) 60\, ohm^{-1}\, cm^{2}\, eq^{-1} $ . What will be the $ pH $ ? (Given : $ \wedge = 400 \, ohm^{-1} \, cm^{2} \, eq^{-1} $ ]
- AMUEEE - 2018
- Electrochemistry
- The electrode potential, $ E^{\circ} $ , for the reduction of $ MnO^{-}_{4} $ to $ Mn^{2+} $ in acidic medium is $ +1.51\, V $ . Which of the following metal(s) will be oxidised? The reduction reactions and standard electrode potentials for $ Zn^{2+}, Ag^{+} $ , and $ Au^{+} $ are given as $ Zn^{2+} (aq) +2e \to Zn(s), E^{\circ} = -0.762\, V $ $ Ag+ (aq) +e {\rightleftharpoons} Ag (s), E^{\circ}=+0.80 \,V $ $ Au^{+} (aq) +e {\rightleftharpoons} Au(s), E^{\circ}+1.69\,V $
- AMUEEE - 2018
- Electrochemistry
- Three particles, two with masses $ m $ and one with mass $ M $ , might be arranged in any of the four configurations shown below. Rank the configurations according to the magnitude of the gravitational force on $ M $ , least to greatest
- AMUEEE - 2018
- Gravitation
- The $ EAN $ value $ y \left[Ti\left(\sigma-C_{6}H_{5}\right)_{2}\left(\pi-C_{5}H_{5}\right)_{2}\right]^{0} $ is
- AMUEEE - 2018
- coordination compounds
View More Questions
Concepts Used:
Relations and functions
A relation R from a non-empty set B is a subset of the cartesian product A × B. The subset is derived by describing a relationship between the first element and the second element of the ordered pairs in A × B.
A relation f from a set A to a set B is said to be a function if every element of set A has one and only one image in set B. In other words, no two distinct elements of B have the same pre-image.
Representation of Relation and Function
Relations and functions can be represented in different forms such as arrow representation, algebraic form, set-builder form, graphically, roster form, and tabular form. Define a function f: A = {1, 2, 3} → B = {1, 4, 9} such that f(1) = 1, f(2) = 4, f(3) = 9. Now, represent this function in different forms.
- Set-builder form - {(x, y): f(x) = y2, x ∈ A, y ∈ B}
- Roster form - {(1, 1), (2, 4), (3, 9)}
- Arrow Representation
