Texts: For what value of the constant is the function f continuous on (-∞, ∞) where c ≠ -5 if a ≤ 3 and f(a) = c√(a^2 - 5) if a > 3?
Hints:
1. The function f will be continuous on the interval (-∞, ∞) if the limit of f as a approaches any value in that interval exists and is equal to the value of f at that point.
2. To find the limit of f as a approaches a certain value, substitute that value into the function and simplify.
3. To find the value of c, consider the conditions for continuity at a = 3.