Let A = {9, 10, 11, 12, 13} and let f: A \(→\) N be defined by f(n) = the highest prime factor of n. Find the range of f.
Solution and Explanation
A = {9, 10, 11, 12, 13}
f: A \(→\) N is defined as
f(n) = The highest prime factor of n
Prime factor of 9 = 3
Prime factors of 10 = 2, 5
Prime factor of 11 = 11
Prime factors of 12 = 2, 3
Prime factor of 13 = 13
∴f(9) = The highest prime factor of 9 = 3
f(10) = The highest prime factor of 10 = 5
f(11) = The highest prime factor of 11 = 11
f(12) = The highest prime factor of 12 = 3
f(13) = The highest prime factor of 13 = 13
The range of f is the set of all f(n), where n ∈A.
∴ Range of f = {3, 5, 11, 13}
Top Questions on Relations and functions
- If the relation \( R \) is given by \[ R = \{(4, 5), (1, 4), (4, 6), (7, 6), (3, 7)\}, \] then find \( R^{-1} \circ R^{-1} \).
- UP Board XII - 2025
- Mathematics
- Relations and functions
- Suppose that \( A = \{2, 3, 4, 5\} \) and a relation \( R \) on \( A \) is defined by \( R = \{(a, b) : a, b \in A, a - b = 12\} \). Then the set \( R \) is
- UP Board XII - 2025
- Mathematics
- Relations and functions
- The relation \( R \), defined by \( R = \{ (T_1, T_2) : T_1 \text{ is similar to } T_2 \} \), in the set \( A \) of all triangles, is
- UP Board XII - 2025
- Mathematics
- Relations and functions
- If \(R^*\) be the set of all non-zero real numbers, then the mapping \(f: R^* \to R^*\) defined by \(f(x) = \frac{1}{x}\) is
- UP Board XII - 2025
- Mathematics
- Relations and functions
- The relation \(R = \{ (a,b): b = a + 2 \}\) defined in the set \(A = \{1, 2, 3, 4, 5\}\) is
- UP Board XII - 2025
- Mathematics
- Relations and functions
Questions Asked in CBSE Class XI exam
Give reasons for the following.
(i) King Tut’s body has been subjected to repeated scrutiny.
(ii) Howard Carter’s investigation was resented.
(iii) Carter had to chisel away the solidified resins to raise the king’s remains.
(iv) Tut’s body was buried along with gilded treasures.
(v) The boy king changed his name from Tutankhaten to Tutankhamun.- CBSE Class XI
- Discovering Tut: The saga Continues
Find the mean deviation about the median for the data
xi 15 21 27 30 35 fi 3 5 6 7 8 - CBSE Class XI
- Mean Deviation
- ‘Have you come back?’ said the woman. ‘I thought that no one had come back.’ Does this statement give some clue about the story? If yes, what is it?
- CBSE Class XI
- The address
- In a class of 60 students, 30 opted for NCC, 32 opted for NSS and 24 opted for both NCC and NSS. If one of these students is selected at random, find the probability that
(i)The student opted for NCC or NSS.
(ii)The student has opted neither NCC nor NSS.
(iii)The student has opted NSS but not NCC- CBSE Class XI
- Axiomatic Approach to Probability
- The following three compound words end in -ship. What does each of them mean?
airship flagship lightship - CBSE Class XI
- We're not afraid to Die if we can all be together
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
