Mathematics

Problem

Consider the rational functions

f(x)=\frac{3x+5}{x-1}, \qquad g(x)=\frac{7-x}{x^{2}-4}.

Answer the following questions. a. (i) Find the domain of

f(x)

. b. (ii) Find the domain of

g(x)

. c. (iii) Explain, without performing any algebraic simplification, why the domain of the difference

h(x)=f(x)-g(x)

must be the intersection of the domains obtained in parts (i) and (ii). d. (iv) Determine the domain of

h(x)

in set–builder form.