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

  • Thread starter JeffNYC
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  • #1
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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

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
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Quadratic formula sounds like a good place to start.
 
  • #3
HallsofIvy
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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.
 
  • #4
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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.
 
  • #5
HallsofIvy
Science Advisor
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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.
 

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