Constant that makes g(x) continous over (-inf,inf)

[JeffNYC]

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

 

[Mathdope]

Quadratic formula sounds like a good place to start.

 

[HallsofIvy]

Actually, I believe that thinking rather than the quadratic formula is a good place to start! Go back and check your equations. You should not have 4c+ 20= 4²+ c! You've dropped a sign.

 

[Mathdope]

Well, yeah, thinking is always good, but he *thought* he should try the quadratic formula and I think he's right in the sense that it will give him the correct answer.

 

[HallsofIvy]

It would be better to think the correct equation first!

My real point was that if he had the right equation, it would be trivial to factor.