Mathematics

Problem

Let

f(x)=\sqrt{x+4}

and

g(x)=\dfrac{2x}{x^{2}-1}

, where each function is taken with its natural domain. Answer the following questions. a. (i) Find the domain of

f

. Express your answer in interval notation. b. (ii) Find the domain of

g

. c. (iii) Determine the domain of

(f+g)(x)

. Give your answer in interval notation. d. (iv) Determine the domain of

(f\,g)(x)

(the product of

f

and

g