Continuity

So to begin our argument, f(x) = $\frac{x^{2}-x-2}{x-2}$ . This function is

defined for all values x except 2, as that causes the denominator of

the argument to be zero. To find "a", you can take the limit of the

function.

$lim_{x=>2} \frac{x^{2}-x-2}{x-2}$

This function can be factored in the numerator to be:

$lim_{x=>2} \frac{x^{2}-x-2}{x-2}$

$lim_{x=>2} \frac{(x+1)\times (x-2)}{x-2}$

$lim_{x=>2} x+1$

At this point, the two may be substituted for x

x+1 = a

2+1 = $\boxed {3}$

Hello,

as for f(x) = (x+1)(x-2) / (x-2) = x+1 , as x not = 2,

since it is continous for all values of x,

f(x) = x + 1 for x=2,

a = f(2) = 2 + 1 =3....

thanks.....