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Math Help - [SOLVED] Domains with e and inverse functions

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    [SOLVED] Domains with e and inverse functions

    Okay so I have what seems to be a fairly simple problem. Find the domain and range of f(x)=(e^x) - 1. Then find the inverse and its domain and range.

    Normally I can do this, but because of e I'm stuck.
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  2. #2
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    Quote Originally Posted by thekrown View Post
    Okay so I have what seems to be a fairly simple problem. Find the domain and range of f(x)=(e^x) - 1. Then find the inverse and its domain and range.

    Normally I can do this, but because of e I'm stuck.
    dom f = R (you should already know this). To find the range of any function you should first draw a graph. It will then be clear that Ran f = (-1, +oo).

    The rule for the inverse function y = f^{-1}(x) is found by solving x = e^y - 1. If you're familiar with logarithms (and I assume you are since you've been set this problem) this equation should be easy to solve. Where do you get stuck?

    Finally, you should know that \text{dom } f^{-1} = \text{ran } f and \text{ran } f^{-1} = \text{dom } f.
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    The domain and range of e^x are all real numbers and all real numbers larger than 0, respectively. That is, in y= e^x x can be any number and y can be any positive number. Now what about y= e^x- 1? If you can calculate e^x for any value of x, can't you then subtract 1 from any number? If y= e^x can be any positive number and then you subtract 1 from it what do you get?
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