Let be a real constant and define f(x)= (x-a)(x+2) (x-a)(x-1) for all in its domain

MATHEMATICS · Single correct · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions

Problem

Let

a

be a real constant and define

f(x)=\frac{(x-a)(x+2)}{(x-a)(x-1)}

for all

x

in its domain. For exactly one of the following values of

a

, the range of

f

excludes the value

\dfrac{5}{2}

. Which value of

a

is it? (a)

\displaystyle a=\frac{5}{3}

(b)

\displaystyle a=\frac{5}{2}

(c)

\displaystyle a=3

(d)

\displaystyle a=1