Find the C (constant) that makes the function g(x) continuous over all real numbers.
g(x) = x^2 - c^2 | if x < 4
= cx + 20 | if x >= 4
The Attempt at a Solution
Since the function is composed of a quadratic and a polynomial they are continuous over all real numbers. Thus, the only possible point of discontinuity lies at x = 4.
lim g(x) as x -> 4 = 4c + 20
I need to make the limit of g(x) as x -> 4 from the left equal to the above limit.
So logically I need to solve for c
c4 + 20 = 4^2 + c^2
Assuming I've thought this through correctly up until this point...I guess I just can't solve the equation. Do I need to use the quadratic formula?