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Math Help - Solving for x given f^-1(x) and secondary equation

  1. #1
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    Solving for x given f^-1(x) and secondary equation

    Hello,
    I am starting out in Calc and this popped up on the first hw/pretest:

    Solve 2 f(x-1)-2=0 for x if f^-1(x)=x^5+x

    I figured f(x-1)=1 and "x=y(y^4+1)" is as far as I got with flipping the inverse.. My algebra is rusty and I'm stuck.
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  2. #2
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    Re: Solving for x given f^-1(x) and secondary equation

    Quote Originally Posted by MickSinclair View Post
    Hello,
    I am starting out in Calc and this popped up on the first hw/pretest:

    Solve 2 f(x-1)-2=0 for x if f^-1(x)=x^5+x

    I figured f(x-1)=1 and "x=y(y^4+1)" is as far as I got with flipping the inverse.. My algebra is rusty and I'm stuck.
    2 f(x-1) - 2 = 0

    f(x-1) = 1 \implies f^{-1}(1) = x-1

    x = f^{-1}(1) + 1 = 1^5 + 1 + 1 = 3
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