Inverse function

English

Noun

1. Template:Lb For a given function f, another function, denoted f⁻¹, that reverses the mapping action of f; Template:Lb given a function $f:X\to Y$, a function $g:Y\to X$ such that, $\mathrm{\forall }x\in X,f(x)=y⟹g(y)=x$. Template:C

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   • 2014, Mark Ryan, Calculus For Dummies, Wiley, 2nd Edition, page 147,

     If $f$ and $g$ are inverse functions, then

     $f^{\prime }(x)=\frac{1}{g^{\prime }(f(x))}$

     In words, this formula says that the derivative of a function, $f$, with respect to $x$, is the reciprocal of the derivative of its inverse function with respect to $f$.

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Further reading

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• Inverse function on Template:W
• Inverse Function on Template:W