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Assertion-1: Let f: R → R and g: R → R be defined by f(x) = sin x and g(x) = x². Then f∘g is not equal to g∘f. Assertion-2: For any x, (f∘g)(x) = f(g(x)) = (g∘f)(x).

1. Assertion-1 is true, Assertion-2 is true; Assertion-2 correctly explains Assertion-1.
2. Assertion-1 is true, Assertion-2 is true; Assertion-2 does not correctly explain Assertion-1.
3. Assertion-1 is false, Assertion-2 is true.
4. Assertion-1 is true, Assertion-2 is false.

Correct answer: Assertion-1 is true, Assertion-2 is false.

Solution

f(g(x)) = sin(x^2) and g(f(x)) = (sin x)^2, which are not equal, so Assertion-1 is true. Assertion-2 claims they are always equal, which is false. So A-1 true, A-2 false.

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