Let and , where and . Answer the following questions about the quotient…

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

Problem

Let

f(x)=x^{2}-4

and

g(x)=x-2

, where

x\in\mathbb R

and

g(x)\neq0

. Answer the following questions about the quotient function. (i) Simplify the expression

\displaystyle \bigl(\tfrac{f}{g}\bigr)(x)

as far as possible. (ii) State the domain of

\displaystyle \bigl(\tfrac{f}{g}\bigr)(x)

, clearly explaining any restrictions that arise both before and after simplification. (iii) Using your simplified form, find the numerical value of

\displaystyle \bigl(\tfrac{f}{g}\bigr)(3)