Consider the rational functions f(x)= 3x+5 x-1

MATHEMATICS · Multi-part · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions

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. (i) Find the domain of

f(x)

. (ii) Find the domain of

g(x)

. (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). (iv) Determine the domain of

h(x)

in set–builder form.