1. ## Continuity Question

Let F(X) =

5x-4, if x is less than or equal to 2

-4x+b, if x is greater than 2

If is a function which is continuous everywhere, then we must have b=_______?

2. Originally Posted by redraider717
Let F(X) =

5x-4, if x is less than or equal to 2

-4x+b, if x is greater than 2

If is a function which is continuous everywhere, then we must have b=_______?
intuitively, what does continuous mean? it means there are no gaps, which means, we want -4x + b to pick up exactly where 5x - 4 left off.

let $f_1(x) = 5x - 4$ and $f_2(x) = -4x + b$

we want, $f_1(2) = f_2(2)$

(yes, technically, $x = 2$ is not in the domain of $f_2(x)$, but we do this because we want to get arbitrary close to $x = 2$)

3. Given $F(x) = \left\{ {\begin{array}{c}
{5x - 4,\;x \le 2} \\
{ - 4x + b,\;x > 2} \\
\end{array}} \right.$

You want: $\lim _{x \to 2^ - } F(x) = \lim _{x \to 2^ + } F(x)$