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Assertion-1: Let f: R → R and g: R → R be defined by f(x) = sin x and g(x) = x^2. 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 true; Assertion-2 does not correctly explain Assertion-1.

Solution

Assertion-1 is true because the composition of functions f(g(x)) results in sin(x^2), while g(f(x)) results in (sin x)^2, which are not equal. Assertion-2 is also true as it correctly states the definitions of the compositions, but it does not explain why the two compositions are different, hence it does not correctly explain Assertion-1.

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