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, ∞)

Answer 1

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?

Answer 2

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