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Math Help - find the inverse

  1. #1
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    find the inverse

    f(x) = e^(x^3) + 3x
    show that f(x) is invertible
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  2. #2
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    Hello,

    f'(x)>0

    Hence f is a strictly monotone function. And thus it is a bijection and is invertible.
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  3. #3
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    thanks so much
    can u help with this part as well

    Let g(y) denote the inverse of f(x). What is the domain and range of g(y)? What is g(e+3)?
    Find g'(e+3)
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  4. #4
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    Quote Originally Posted by rphagoo View Post
    thanks so much
    can u help with this part as well

    Let g(y) denote the inverse of f(x).

    What is the domain and range of g(y)? the range and domain of f(x)

    What is g(e+3)?

    f(1) = e+3 , so g(e+3) = 1

    Find g'(e+3)

    \textcolor{red}{g'(e+3) = \frac{1}{f'(1)}}
    ...
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  5. #5
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    thanks so much!
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