(a)

The function .

Domain of sine function is all real numbers.

Here, can exist for all real numbers.

Domain of the function is all real numbers.

(b)

The function .

The function is a square root function.

Therefore, value inside the function cannot be negative.

.

Apply natural logarithm on each side.

Domain of the function is .

(a) Domain of the function is all real numbers.

(b) Domain of the function is .