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Homework Help: Inverse problemshelp please!

  1. Aug 30, 2010 #1
    1. The problem statement, all variables and given/known data
    1) When a camera flash goes off, the batteries immediately begin to recharge the flash's capacitor, which stores electric charge given by the following. (The maximum charge capacity is M and t is measured in seconds.)

    Q(t) = M(1 - e-t/a)

    (a) Find the inverse of this function and explain its meaning.

    2. Let f(x) = 2 + x2 + tan(πx/2), where -1 < x < 1.
    (a) Find f(f -1(4)).

    2. Relevant equations


    3. The attempt at a solution
    (1) Q = M(1 - e^-t/a)
    Q/M = 1 - e^-t/a
    e^-t/a = 1 - Q/M
    -t/a (ln e) = ln(1 - Q/M)
    -t/a = ln(1 - Q/M)
    t = -a[ln(1 - Q/M)]

    That's not right.

    (#2.) x = 2 + y^2 + tan(π*y/2)
    4 = 2 + y^2 + tan(π*y/2)
    *plug into wolfram alpha... y~0.642
    f(x) = 2 + x2 + tan(πx/2) original formula
    f(.642)= 2 + (.642^2) + tan (.642π/2)

    That's not right either.

    I'm not really seeing where I went wrong in either of them..any help is appreciated.
  2. jcsd
  3. Aug 30, 2010 #2


    Staff: Mentor

    Why do you think this is wrong? This is what I got, but I am uncertain about the equation you wrote. I think you meant Q = M(1 - e^(-t/a)). If that is what you meant, then your answer is correct. However, you did not explain the meaning of the inverse here.
    Yes, you have an error here. You have the right idea, but probably made an error when you calculated f(.642). You should get a final answer that is close to 4. You'll get better results with more precision in your value for f-1(4), which I took as 0.64216.
  4. Aug 30, 2010 #3
    I think it's wrong because it's an online homework assignment and it told me that my answer was wrong. :/ That is the right equation. Sorry, I got the explanation part right but just copied the whole question.
    Ah, gotcha. Thanks.
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