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Composition of Functions Video Lecture | Mathematics (Maths) Class 12 - JEE

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FAQs on Composition of Functions Video Lecture - Mathematics (Maths) Class 12 - JEE

1. What is the definition of composition of functions?
Ans. The composition of functions is a mathematical operation that combines two functions to create a new function. It involves applying one function to the output of another function.
2. How do you express the composition of two functions?
Ans. The composition of two functions f and g is denoted as (f ∘ g)(x) or f(g(x)). This means that the output of g is used as the input for f.
3. Can you provide an example of composition of functions?
Ans. Sure! Let's consider f(x) = 2x and g(x) = x + 3. To find the composition (f ∘ g)(x), we substitute g(x) into f(x), giving us f(g(x)) = 2(x + 3). Simplifying further, we get f(g(x)) = 2x + 6.
4. What is the order of operations in composition of functions?
Ans. When composing functions, we follow the order of operations from right to left. This means that the innermost function is applied first, and then the result is used as the input for the outer function.
5. Are there any restrictions or conditions for the composition of functions?
Ans. Yes, there are a few conditions to consider. The output of the inner function must be within the domain of the outer function. In addition, the composition of functions is not commutative, meaning that (f ∘ g)(x) may not be the same as (g ∘ f)(x). It is important to check the domains and ranges of the functions involved to ensure the composition is valid.
204 videos|288 docs|139 tests

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