The function f : N → R is defined by f n = 2 n . The range of the function is

a subset of set of all even positive integers

the set of all even positive integers

Show that the function f : N → N defined by f n = n + 1 is not onto, by drawing arrow diagrams.

Given, the function f : N → N defined by f n = n + 1 . N = 1 , 2 , 3 , 4 , 5 , 6 , . . . . . . . f 1 = 1 + 1 = 2 f 2 = 2 + 1 = 3 f 3 = 3 + 1 = 4 f 4 = 4 + 1 = 5 f 5 = 5 + 1 = 6 Thus, f = 1 , 2 , 2 , 3 , 3 , 4 , 4 , 5 , 5 , 6 , . . . . . . . . . . . . Different elements have different images. Here, the range is not equal to the codomain. Therefore, the given function is not an onto function.

The function f : N → R is defined by f n = 2 n . The range of the function is

a subset of set of all even positive integers

the set of all even positive integers

E M B I B E

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 1 - Relations and Functions>Exercise>Q 2

MEDIUM

10th Tamil Nadu Board

IMPORTANT

Earn 100

If $(x - 1, y + 4) = (1, 2)$ , then the values of $x$ and $y$ are

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Important Questions on Relations and Functions

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10th Tamil Nadu Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 1 - Relations and Functions>Exercise>Q 3

If

A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6}

and

D = {5, 6, 7, 8}

then state which of the following statement is true.

EASY

10th Tamil Nadu Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 1 - Relations and Functions>Exercise>Q 4

Write the set builder form of

A = {- 1, 1}

.

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10th Tamil Nadu Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 1 - Relations and Functions>Exercise>Q 5

A relation between

A

and

B

is

EASY

10th Tamil Nadu Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 1 - Relations and Functions>Exercise>Q 6

The function

f : N \to R

is defined by

f (n) = 2^{n}

. The range of the function is

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10th Tamil Nadu Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 1 - Relations and Functions>Exercise>Q 7

The range of the relation

R = {(x, x^{2}) ∣ x

is a prime number less than

13}

is

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10th Tamil Nadu Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 1 - Relations and Functions>Exercise>Q 8

If $A = \{1, 2, 3, 4\}$ and $B = \{a, b, c\}$ , $f = \{(1, a), (2, a), (3, b), (4, c)\}$ , where $f$ is the function from $A \to B$ , then find out which type of function is $f$ .