The range of the function $f(x)=\sqrt{3-x}+\sqrt{2+x}$ is:
- $[2 \sqrt{2}, \sqrt{11}]$
- $[\sqrt{5}, \sqrt{10}]$
- $[\sqrt{5}, \sqrt{13}]$
- $[\sqrt{2}, \sqrt{7}]$
The Correct Option is B
Solution and Explanation
So , the correct option is (B) : $[\sqrt{5}, \sqrt{10}]$
Top Questions on Functions
- Consider the sets $A = \{(x, y) \in \mathbb{R} \times \mathbb{R} : x^2 + y^2 = 25\}$, $B = \{(x, y) \in \mathbb{R} \times \mathbb{R} : x^2 + 9y^2 = 144\}$, $C = \{(x, y) \in \mathbb{Z} \times \mathbb{Z} : x^2 + y^2 \leq 4\}$, and $D = A \cap B$. The total number of one-one functions from the set $D$ to the set $C$ is:
- Let $f, g: (1, \infty) \rightarrow \mathbb{R}$ be defined as $f(x) = \frac{2x + 3}{5x + 2}$ and $g(x) = \frac{2 - 3x}{1 - x}$. If the range of the function $fog: [2, 4] \rightarrow \mathbb{R}$ is $[\alpha, \beta]$, then $\frac{1}{\beta - \alpha}$ is equal to
- Given the function \( F(x) = |\sin(3x)| - \cos(3x) \), for \( \frac{\pi}{6} \leq x \leq \frac{\pi}{3} \), find \( f' \left( \frac{\pi}{4} \right) \).
- KEAM - 2025
- Mathematics
- Functions
- If \( f(x) = \sqrt{x - 3} + 4 \sqrt{5 - x} \), find the domain of \( f(x) \).
- KEAM - 2025
- Mathematics
- Functions
- Given the function \( h(x) = f(g(x)) \), where \( f(x) = f'(x) = 3 \), and \( g(x) = 9 \), find \( g'(3) \), \( f'(3) \), and \( h'(3) \).
- KEAM - 2025
- Mathematics
- Functions
Questions Asked in JEE Main exam
- A force of 49 N acts tangentially at the highest point of a sphere (solid of mass 20 kg) kept on a rough horizontal plane. If the sphere rolls without slipping, then the acceleration of the center of the sphere is:
- JEE Main - 2025
- Quantum Mechanics
Match List-I with List-II: List-I
- JEE Main - 2025
- Classification Of Organic Compounds
- Three identical spheres of mass m, are placed at the vertices of an equilateral triangle of length a. When released, they interact only through gravitational force and collide after a time T = 4 seconds. If the sides of the triangle are increased to length 2a and also the masses of the spheres are made 2m, then they will collide after ______ seconds.
- JEE Main - 2025
- Gravitation
- A photo-emissive substance is illuminated with a radiation of wavelength $ \lambda_i $ so that it releases electrons with de-Broglie wavelength $ \lambda_e $. The longest wavelength of radiation that can emit photoelectron is $ \lambda_0 $. Expression for de-Broglie wavelength is given by : (m : mass of the electron, h : Planck's constant and c : speed of light)
- JEE Main - 2025
- Photoelectric Effect
The dimension of $ \sqrt{\frac{\mu_0}{\epsilon_0}} $ is equal to that of: (Where $ \mu_0 $ is the vacuum permeability and $ \epsilon_0 $ is the vacuum permittivity)
- JEE Main - 2025
- Electromagnetic waves
Concepts Used:
Functions
A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. Let A & B be any two non-empty sets, mapping from A to B will be a function only when every element in set A has one end only one image in set B.
Kinds of Functions
The different types of functions are -
One to One Function: When elements of set A have a separate component of set B, we can determine that it is a one-to-one function. Besides, you can also call it injective.
Many to One Function: As the name suggests, here more than two elements in set A are mapped with one element in set B.
Moreover, if it happens that all the elements in set B have pre-images in set A, it is called an onto function or surjective function.
Also, if a function is both one-to-one and onto function, it is known as a bijective. This means, that all the elements of A are mapped with separate elements in B, and A holds a pre-image of elements of B.
Read More: Relations and Functions