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.

Options

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

A

Explanation

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 .