To determine

To find:

(a) Domain of the given function g.

(b) Domain of the given function f.

Answer

(a) The domain of the given function is (2,∞).

(b) Domain of the given function is the set of all real numbers.

Explanation

a) Given:gt=10t-100.

The given function is square root function, which is defined only for non-negative values. Therefore g is defined if 10t-100>0, i.e., 10t>102 if and only if t>2. The domain of the given function is (2,∞).

b) Given: ft=sin⁡(et-1)

Since sine function is defined for all real numbers, et-1 belongs to the set of all real numbers i.e., et belongs to the set of all real numbers. Since exponential function is defined for all real numbers, Domain of the given function is the set of all real numbers.

Conclusion:

(a) The domain of the given function is (2,∞).

(b) Domain of the given function is the set of all real numbers.