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Questions and Answers
क्या संबंध R = {(1, 3), (2, 4), (3, 6)} एक कार्य है?
क्या संबंध R = {(1, 3), (2, 4), (3, 6)} एक कार्य है?
फ़ंक्शन g(x) = x^2 क्या एक कार्य है?
फ़ंक्शन g(x) = x^2 क्या एक कार्य है?
संबंध R = {(1, 3), (2, 4), (3, 6)} का क्रमचय और सीमा क्या है?
संबंध R = {(1, 3), (2, 4), (3, 6)} का क्रमचय और सीमा क्या है?
किसे कहा जाता है कि रिश्ता है, जबकि एक संबंध एक सेट के क्रमबद्ध जोड़ों का होता है?
किसे कहा जाता है कि रिश्ता है, जबकि एक संबंध एक सेट के क्रमबद्ध जोड़ों का होता है?
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क्या एक संबंध को वहीं कहा जाता है जो एकल मूल्यवाला होता है?
क्या एक संबंध को वहीं कहा जाता है जो एकल मूल्यवाला होता है?
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किसे 'निर्भर स्थिति' कहा जाता है?
किसे 'निर्भर स्थिति' कहा जाता है?
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यहाँ, y = 3x + 2 के संबंध के डोमेन क्या है?
यहाँ, y = 3x + 2 के संबंध के डोमेन क्या है?
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Study Notes
Relation and Function
Relations and functions are fundamental concepts in mathematics that help us understand the way data and variables interact. In this article, we will explore the concepts of domain and range, as well as the relationship between relations and functions.
Domain and Range
The domain of a relation is the set of all possible inputs, while the range is the set of all possible outputs. To find the domain of a relation, we need to determine the values that can be used for the independent variable (e.g., x) in the relation. Similarly, to find the range of a relation, we need to determine the values that can be used for the dependent variable (e.g., y).
For example, consider the relation y = 3x + 2. The domain of this relation is all real numbers because there are no restrictions on the input, x. The range of the relation is all real numbers greater than or equal to 4 (i.e., y >= 4) because 3x + 2 will always be greater than or equal to 4 if x is a real number.
Relation and Function
A relation is a set of ordered pairs, while a function is a relation that has the property of being single-valued. In other words, a function maps each value of the input to only one value of the output, whereas a relation can map multiple values of the input to the same value of the output.
For example, consider the relation R = {(1, 3), (2, 4), (3, 6)}. This relation is not a function because the input value 2 maps to the output value 4, while the input value 3 maps to the output value 6. However, the relation y = 2x + 1 is a function because for each input value of x, there is a unique output value of y.
Relation and Function: Examples and Exercises
- Find the domain and range of the relation R = {(1, 3), (2, 4), (3, 6)}.
- Determine if the relation R = {(1, 3), (2, 4), (3, 6)} is a function.
- Find the domain and range of the function f(x) = 3x + 2.
- Determine if the function g(x) = x^2 is a function.
Conclusion
Understanding the concepts of domain and range, as well as the relationship between relations and functions, is crucial for mastering mathematical concepts. By studying these ideas, we can better understand how variables interact and how to analyze data more effectively.
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Description
Explore the concepts of domain and range in relation to the relationship between relations and functions. Learn about the properties of relations and functions, and practice finding domains and ranges, as well as determining if given relations are functions.
