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Math Help - Polynomials and inverses

  1. #1
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    Polynomials and inverses

    If h(x)=x^3 +2x+1 has an inverse h^{-1} on \mathbb{R} , how would you find the value of (h^{-1})')(y) at the points corresponding to x=0,1,-1 ?
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  2. #2
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    Quote Originally Posted by frenchguy87 View Post
    If h(x)=x^3 +2x+1 has an inverse h^{-1} on \mathbb{R} , how would you find the value of (h^{-1})')(y) at the points corresponding to x=0,1,-1 ?

    By a well-known theorem, (h^{-1})'=\frac{1}{h'} , with the proper variables in each, so in this case (h^{-1})'(1)=\frac{1}{h'(0)}=\frac{1}{2\cdot 0^2+2}=\frac{1}{2} , since h(0)=1\Longleftrightarrow h^{-1}(1)=0 ...now you ty to do the other ones.

    Tonio
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