Algebra of Continuous Functions

# Algebra of Continuous Functions Video Lecture | Mathematics (Maths) Class 12 - JEE

## Mathematics (Maths) Class 12

204 videos|288 docs|139 tests

## FAQs on Algebra of Continuous Functions Video Lecture - Mathematics (Maths) Class 12 - JEE

 1. What is the algebra of continuous functions?
Ans. The algebra of continuous functions is a mathematical concept that focuses on the properties and operations of continuous functions. It deals with the addition, subtraction, multiplication, and division of continuous functions, allowing for the manipulation and analysis of these functions using algebraic techniques.
 2. How are continuous functions added or subtracted?
Ans. When adding or subtracting continuous functions, we simply add or subtract the corresponding values of the functions at each point. For example, if we have two continuous functions f(x) and g(x), the sum of the functions (f+g)(x) or the difference (f-g)(x) can be obtained by adding or subtracting the values of f(x) and g(x) at each x.
 3. Can continuous functions be multiplied or divided?
Ans. Yes, continuous functions can be multiplied and divided. When multiplying two continuous functions f(x) and g(x), we multiply their corresponding values at each point. Similarly, when dividing two continuous functions, we divide their corresponding values at each point, as long as the denominator function is not equal to zero at any point.
 4. What are the properties of the algebra of continuous functions?
Ans. The algebra of continuous functions has several important properties, including closure under addition, subtraction, multiplication, and division. This means that the sum, difference, product, and quotient of continuous functions will also be continuous functions. Additionally, the algebra of continuous functions follows the usual rules of algebra, such as the distributive property and the commutative property.
 5. How is the algebra of continuous functions useful in analysis?
Ans. The algebra of continuous functions is a fundamental tool in mathematical analysis. It allows us to manipulate and analyze continuous functions using familiar algebraic techniques, making it easier to study their properties and behavior. By applying the algebraic operations to continuous functions, we can solve equations, find roots, determine limits, and explore the relationships between different functions.

## Mathematics (Maths) Class 12

204 videos|288 docs|139 tests

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