Calculus

Give the domain of each of the functions listed below :
a) f(x)= ln (tanh^-1 (x))
b) g(x) = cos ^-1 (e^x)

I just don't know how to set them up to solve for x ...I'm doing a Calc course online on my own, and would really appreciate the help :)
Thanks

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asked by Katie
  1. a) There can be no log of a negative number or zero, so
    tanh^-1(x) > 0
    That requires x > 0, since
    tanh(x) > 0 for x > 0

    b) e^x must be between -1 and 1, since the cosine function is between those extremes.

    e^x cannot be <0 for any x
    if e^x => 0, x => -infinity
    If e^x = 1
    x = ln(1) = 0

    -infinity < x < 0

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    posted by drwls

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