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3.Composition of Functions
Class 11 • Mathematics • NCERT
Composition of Functions
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This lesson explains the composition of functions as prescribed by NCERT Class 11. Students learn how two functions combine to form a new function and understand the conditions under which composition is defined.
Lesson Objectives
- Understand composition of functions.
- Learn notation (f ∘ g).
- Apply domain conditions correctly.
- Solve NCERT-style problems.
1. Meaning of Composition
Let f : A → B and g : B → C be two functions. The composition of f and g is a function from A to C.
(f ∘ g)(x) = f(g(x))
2. Order of Composition
In general, composition of functions is not commutative.
f ∘ g ≠ g ∘ f
3. Domain of Composite Function
The domain of (f ∘ g) consists of all x such that:
x ∈ Domain of g and g(x) ∈ Domain of f
⚠️ This is a very important NCERT exam point.
4. Simple NCERT Examples
Let f(x) = x + 2, g(x) = 3x
(f ∘ g)(x) = f(3x) = 3x + 2
(g ∘ f)(x) = g(x + 2) = 3x + 6
5. Composition with Identity Function
Let I(x) = x be the identity function. Then:
f ∘ I = I ∘ f = f
Practice Questions (NCERT)
- Define composition of functions.
- Write the formula for (f ∘ g)(x).
- Is composition commutative?
- Find (f ∘ g)(x) if f(x) = x² and g(x) = x + 1.
- Find (g ∘ f)(x) for the same functions.
- State the condition for domain of (f ∘ g).
- What is the identity function?
- Find (f ∘ I)(x).
- Can composition always be defined?
- Is this topic part of NCERT Class 11 syllabus?
✅ Show Answer Key
- Combining two functions to form a new function
- (f ∘ g)(x) = f(g(x))
- No
- (x + 1)²
- x² + 1
- g(x) must lie in domain of f
- I(x) = x
- f(x)
- No
- Yes
© Aviate Learning – Relations & Functions (NCERT Class 11)