- #1

JeffNYC

- 26

- 0

## Homework Statement

Find the C (constant) that makes the function g(x) continuous over all real numbers.

## Homework Equations

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?

Thanks Guys,

Jeff