Mathematics

Problem

Let

f(x) = 5 - |x - 2|

and

g(x) = |x + 1|, x \in R

. If

f(x)

attains maximum value at

\alpha

and

g(x)

attains minimum value at

\beta

, then

\lim_{x \rightarrow -\alpha\beta} \frac{(x-1)(x^2-5x+6)}{x^2-6x+8}

is equal to: (a)

\frac{1}{2}

(b)

-\frac{3}{2}

(c)

-\frac{1}{2}

(d)

\frac{3}{2}