Question:
Let f(x) = [x], x ∈ R, where [x] denotes the greatest integer ≤ x. Then the images of the elements -4.6 and 2.7 are respectively
Let f(x) = [x], x ∈ R, where [x] denotes the greatest integer ≤ x. Then the images of the elements -4.6 and 2.7 are respectively
Updated On: Apr 4, 2025
- -5, 2
- -5, 3
- -4, 2
- -3, 3
- -4, 3
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
We are given the function f(x) = [x], where [x] denotes the greatest integer less than or equal to x.
For x = -4.6, the greatest integer less than or equal to -4.6 is -5. So, f(-4.6) = -5.
For x = 2.7, the greatest integer less than or equal to 2.7 is 2. So, f(2.7) = 2.
The answer is -5, 2.
Was this answer helpful?
0
0
Top Questions on Relations and functions
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is:
- JEE Main - 2025
- Mathematics
- Relations and functions
- Let $f: A \to B$ be defined by $f(x) = \frac{x - 2}{x - 3}$, where $A = \mathbb{R} - \{3\}$ and $B = \mathbb{R} - \{1\}$. Discuss the bijectivity of the function.
- CBSE CLASS XII - 2025
- Mathematics
- Relations and functions
- Let \( R \) be a relation defined on a set \( \mathbb{N} \) of natural numbers such that \( R = \{(x, y) : xy \text{ is a square of a natural number}, x, y \in \mathbb{N} \} \). Determine if the relation \( R \) is an equivalence relation.
- CBSE CLASS XII - 2025
- Mathematics
- Relations and functions
- Show that the function \( f : \mathbb{R} \to \mathbb{R} \) defined by \( f(x) = 4x^3 - 5 \), \( \forall x \in \mathbb{R} \), is one-one and onto.
- CBSE CLASS XII - 2025
- Mathematics
- Relations and functions
- If $f(x) = -2x^2$, then the correct statement is:
- CBSE CLASS XII - 2025
- Mathematics
- Relations and functions
View More Questions
Questions Asked in KEAM exam
- Benzene when treated with Br\(_2\) in the presence of FeBr\(_3\), gives 1,4-dibromobenzene and 1,2-dibromobenzene. Which type of reaction is this?
- KEAM - 2025
- Haloalkanes and Haloarenes
- 10 g of (90 percent pure) \( \text{CaCO}_3 \), treated with excess of HCl, gives what mass of \( \text{CO}_2 \)?
- KEAM - 2025
- Stoichiometry and Stoichiometric Calculations
- Evaluate the following limit: $ \lim_{x \to 0} \frac{1 + \cos(4x)}{\tan(x)} $
- KEAM - 2025
- Limits
- Given that \( \mathbf{a} \times (2\hat{i} + 3\hat{j} + 4\hat{k}) = (2\hat{i} + 3\hat{j} + 4\hat{k}) \times \mathbf{b} \), \( |\mathbf{a} + \mathbf{b}| = \sqrt{29} \), \( \mathbf{a} \cdot \mathbf{b} = ? \)
- KEAM - 2025
- Vector Algebra
- In an equilateral triangle with each side having resistance \( R \), what is the effective resistance between two sides?
- KEAM - 2025
- Combination of Resistors - Series and Parallel
View More Questions