For what value of the constant c is the function f continuous on ( -infinity , infinity ) where
f(x)={cx+3 if x \in (-infinity,8]
{cx^2-3 if x \in (8,infinity)

Question

For what value of the constant c is the function f continuous on ( -infinity , infinity ) where 
f(x)={cx+3 if x \in (-infinity,8]
        {cx^2-3 if x \in (8,infinity)

anonymous · Answer

Those "\in"s should be $$\in$$

anonymous · Answer

The function is continuous if
$$\lim_{x\to8^-}f(x)=\lim_{x\to8^+}f(x)$$
and if $f(8)=8c+3$.

Use the limit equation to solve for $c$.

anonymous · Answer

That's what I tried doing...I got 8c+3, then 64c-3 for the other side. Set the two equations together and I got c=9.333. I put that in to my homework thing and it says I have the wrong answer.

anonymous · Answer

I don't think your $c$ is right.

anonymous · Answer

$$\begin{align*}
8c+3&=64c-3\
56c&=6\
c&=\frac{3}{28}
\end{align*}$$

anonymous · Answer

oh wow, I divided by the wrong side, like I had the c attached to 6. That was an idiot move. Lemme try 3/28.

It worked. Thanks!

anonymous · Answer

You're welcome!