f(x) = -2x +b, if x<-4
-96/x-b, if >(or equal to) -4
There are exactly two values for b which make f(x) a continuous function at x=-4. The one with the greater asolute value is b=______
$\displaystyle f(-4) = -\frac{96}{(-4)-b}$
from the left side of $\displaystyle x = -4$, $\displaystyle f(x)$ gets close to $\displaystyle -2(-4) + b$
both sides should be equal for $\displaystyle f(x)$ to be continuous.
solve the equation for b ...
$\displaystyle -\frac{96}{(-4)-b} = -2(-4) + b$