This question has been annoying me for too long:
Let f(x) be an invertible function, with domain R. Let p(x) = 1 / ( 1 + f(x) ). Find p^−1(x), in terms of f^−1.
Help is greatly appreciated :D
Let f(x) be an invertible function, with domain R. Let p(x) = 1 / ( 1 + f(x) ). Find p^−1(x), in terms of f^−1.
Help is greatly appreciated :D
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x=1/(1+f(p^-1(x)))
1/x=1+f(p^-1(x))
1/x-1=f(p^-1(x))
f^-1((1-x)/x)=p^-1(x)
1/x=1+f(p^-1(x))
1/x-1=f(p^-1(x))
f^-1((1-x)/x)=p^-1(x)