Question

Find c such that the function :
f(x)=x^2−6 xc is continuous everywhere. C=?

Answer 1

Set them equal to each other. There's a theorem that explains this but i 4got the name.

Answer 2

\[f(x)=\begin{cases}x^2-6 &\text{for $x<c$}\\
8x-22& \text{for $x>c$}\end{cases}\]
I'm sure you mean ≤ or ≥ for one of those pieces, so I'll assume you meant
\[f(x)=\begin{cases}x^2-6 &\text{for $x\le c$}\\
8x-22& \text{for $x>c$}\end{cases}\]
For f(x) to be continuous at c, the following must be satisfied:
\[\lim_{x\to c^-}f(x)=\lim_{x\to c^+}f(x)\]
Do you know where to take it from here?