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

  1. Feb 13, 2008 #1
    1. The problem statement, all variables and given/known data

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


    2. Relevant equations

    g(x) = x^2 - c^2 | if x < 4

    = cx + 20 | if x >= 4

    3. 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
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 13, 2008 #2
    Quadratic formula sounds like a good place to start.
     
  4. Feb 13, 2008 #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.
     
  5. Feb 13, 2008 #4
    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.
     
  6. Feb 14, 2008 #5

    HallsofIvy

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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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