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

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

1. What is the composition of functions?
Ans. The composition of functions is an operation that combines two functions to create a new function. It involves applying one function to the output of another function. The composition of two functions f and g is represented as (f ∘ g)(x) and is defined as (f ∘ g)(x) = f(g(x)).
2. How do you find the composition of functions?
Ans. To find the composition of functions, you need to substitute the output of one function into the input of another function. Let's say you have two functions f(x) and g(x). To find the composition (f ∘ g)(x), you evaluate g(x) first, and then substitute that result into f(x).
3. What is the importance of composition of functions?
Ans. The composition of functions is important as it allows us to combine functions and create new functions that can model more complex relationships between variables. It provides a way to build more sophisticated mathematical models by combining simpler functions.
4. Can you give an example of the composition of functions?
Ans. Sure! Let's consider two functions f(x) = 2x + 3 and g(x) = x^2. To find the composition (f ∘ g)(x), we first evaluate g(x) by substituting x into the function: g(x) = x^2. Then, we substitute the result into f(x): (f ∘ g)(x) = f(g(x)) = f(x^2) = 2(x^2) + 3.
5. Are there any properties or rules related to the composition of functions?
Ans. Yes, several properties and rules are associated with the composition of functions. For example, the composition of functions is associative, meaning that for three functions f, g, and h, (f ∘ g) ∘ h = f ∘ (g ∘ h). Additionally, the identity function serves as the identity element for composition, meaning that for any function f, f ∘ I = I ∘ f = f, where I represents the identity function.
204 videos|288 docs|139 tests

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