For what value of the constant c is the function f continuous on ( −∞, ∞) where
f( a ) =
⎨c a + 9 if a ∈ (−∞, 7]
{ c a^ 2 − 9 if a ∈ (7, ∞)

Question

For what value of the constant c is the function f continuous on ( −∞, ∞) where 
f( a ) =
⎨c a + 9     if     a ∈ (−∞, 7]        
 { c a^ 2 − 9  if     a ∈ (7, ∞)

turingtest · Answer

what value of $c$ makes$$f(a)=\left\{\begin{array}~ca+9~~~~~if~~~~a\le7\ca^2-9~~~if~~~~a>7\end{array}\right.$$continuous for all $a\in\mathbb R$ ?
is that the question?

turingtest · Answer

a function is continuous at a point p if$$\lim_{x\to p^+}f(x)=\lim_{x\to p^-}f(x)=f(p)$$