Let two functions R→R, R→R are defined as f(a) g(a)
Let two functions f: R→R, g: R→R are defined as
f(a) = a2
g(a) = a+1
then choose the correct option.
- A.
Composition of f(a), g(a) is commutative
- B.
Composition of f(a), g(a) is not commutative
- C.
Composition of f(a), g(a) is commutative and equivalent to f(a2 + 1)
- D.
Composition of f(a), g(a) is commutative and equivalent to (a2 + 1)
Attempted by 103 students.
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Correct answer: B
Compute f∘g: f(g(a)) = f(a+1) = (a+1)^2 = a^2 + 2a + 1
Compute g∘f: g(f(a)) = g(a^2) = a^2 + 1
Compare the two results:
f(g(a)) = a^2 + 2a + 1
g(f(a)) = a^2 + 1
Conclusion: The two compositions are not equal for general a (they are equal only when a = 0), so composition of f and g is not commutative.