Statement-1: The function f(x) given by `f(x)=sin^(-1){log(x+sqrt(x^(2)+1))}` is an odd function. Statement:2 The composition of two odd functions is an odd function.A. Statement-1 is True, Statement-2 is True, statement-2 is a correct explanation for the statement-1 .B. Statement-1 is True, Statement-2 is True, statement-2 is not a correct explanation for the statement-1 .C. Statement-1 is True, Statement-2 is False.D. Statement-1 is False , Statement-2 is True.

Statement-1: The function f(x) given by `f(x)=sin^(-1){log(x+sqrt(x^(2

1.	Statement-1: The function f(x) given by `f(x)=sin^(-1){log(x+sqrt(x^(2)+1))}` is an odd function. Statement:2 The composition of two odd functions is an odd function.A. Statement-1 is True, Statement-2 is True, statement-2 is a correct explanation for the statement-1 .B. Statement-1 is True, Statement-2 is True, statement-2 is not a correct explanation for the statement-1 .C. Statement-1 is True, Statement-2 is False.D. Statement-1 is False , Statement-2 is True.
Answer» Correct Answer - A Let `phi(x) and Psi(x)` be two odd functions. Then, `(phi 0 Psi)(-x)=phi(Psi(-x))=phi(-Psi(x))=-phi(Psi(x))=-phi0Psi(x)` `implies phi 0 Psi` is an odd function. So,statement-2 is true. If `phi(x)=sin^(-1)x and Psi(x)=log(x+sqrt(x^(2)+1))`. Then, `phi` and `Psi` are odd functions such that `phi 0 Psi=f`. Hence, f is an odd function. so, statement-1 is true. Also, statement-2 is a correct explanation for statement-1 .

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