Para cada n° real x ≠ 1, define-se f(x) = x/(x - 1). Então f(f(x)) é sempre igual a:
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Bom dia Eric!
Solução!
Função f(x) composta com f(x).
![f(x)= \dfrac{x}{x-1}\\\\\\\
f(f(x))\\\\\\
f(x)= \dfrac{x}{x-1}\\\\\\f(f(x))= \dfrac{ \dfrac{x}{x-1} }{ \dfrac{x}{x-1} -1}\\\\\\\
f(f(x))=\dfrac{ \dfrac{x}{x-1} }{ \dfrac{x-1(x-1)}{x-1} }\\\\\\\
f(f(x))=\dfrac{ \dfrac{x}{x-1} }{ \dfrac{x+(-x+1}{x-1} }\\\\\\\
f(f(x))=\dfrac{ \dfrac{x}{x-1} }{ \dfrac{x-x+1)}{x-1} }\\\\\\\
f(f(x))=\dfrac{ \dfrac{x}{x-1} }{ \dfrac{1}{x-1} }\\\\\\\
f(f(x))=\dfrac{ x }{x-1}\times \frac{x-1}{1} \\\\\\\
f(f(x))=\dfrac{ x }{1} \\\\\\\
f(f(x))=x](https://tex.z-dn.net/?f=f%28x%29%3D+%5Cdfrac%7Bx%7D%7Bx-1%7D%5C%5C%5C%5C%5C%5C%5C%0Af%28f%28x%29%29%5C%5C%5C%5C%5C%5C%0A+f%28x%29%3D+%5Cdfrac%7Bx%7D%7Bx-1%7D%5C%5C%5C%5C%5C%5Cf%28f%28x%29%29%3D+%5Cdfrac%7B+%5Cdfrac%7Bx%7D%7Bx-1%7D+%7D%7B+%5Cdfrac%7Bx%7D%7Bx-1%7D+-1%7D%5C%5C%5C%5C%5C%5C%5C%0Af%28f%28x%29%29%3D%5Cdfrac%7B+%5Cdfrac%7Bx%7D%7Bx-1%7D+%7D%7B++%5Cdfrac%7Bx-1%28x-1%29%7D%7Bx-1%7D+%7D%5C%5C%5C%5C%5C%5C%5C%0Af%28f%28x%29%29%3D%5Cdfrac%7B+%5Cdfrac%7Bx%7D%7Bx-1%7D+%7D%7B++%5Cdfrac%7Bx%2B%28-x%2B1%7D%7Bx-1%7D+%7D%5C%5C%5C%5C%5C%5C%5C%0A%0Af%28f%28x%29%29%3D%5Cdfrac%7B+%5Cdfrac%7Bx%7D%7Bx-1%7D+%7D%7B++%5Cdfrac%7Bx-x%2B1%29%7D%7Bx-1%7D+%7D%5C%5C%5C%5C%5C%5C%5C%0Af%28f%28x%29%29%3D%5Cdfrac%7B+%5Cdfrac%7Bx%7D%7Bx-1%7D+%7D%7B++%5Cdfrac%7B1%7D%7Bx-1%7D+%7D%5C%5C%5C%5C%5C%5C%5C%0Af%28f%28x%29%29%3D%5Cdfrac%7B+x+%7D%7Bx-1%7D%5Ctimes+%5Cfrac%7Bx-1%7D%7B1%7D+%5C%5C%5C%5C%5C%5C%5C%0A%0Af%28f%28x%29%29%3D%5Cdfrac%7B+x+%7D%7B1%7D+%5C%5C%5C%5C%5C%5C%5C%0Af%28f%28x%29%29%3Dx "f(x)= \dfrac{x}{x-1}\\\\\\\
f(f(x))\\\\\\
f(x)= \dfrac{x}{x-1}\\\\\\f(f(x))= \dfrac{ \dfrac{x}{x-1} }{ \dfrac{x}{x-1} -1}\\\\\\\
f(f(x))=\dfrac{ \dfrac{x}{x-1} }{ \dfrac{x-1(x-1)}{x-1} }\\\\\\\
f(f(x))=\dfrac{ \dfrac{x}{x-1} }{ \dfrac{x+(-x+1}{x-1} }\\\\\\\
f(f(x))=\dfrac{ \dfrac{x}{x-1} }{ \dfrac{x-x+1)}{x-1} }\\\\\\\
f(f(x))=\dfrac{ \dfrac{x}{x-1} }{ \dfrac{1}{x-1} }\\\\\\\
f(f(x))=\dfrac{ x }{x-1}\times \frac{x-1}{1} \\\\\\\
f(f(x))=\dfrac{ x }{1} \\\\\\\
f(f(x))=x")
Bom dia!
Bons estudos!
Solução!
Função f(x) composta com f(x).
Bom dia!
Bons estudos!
EricLopes:
porque fica funçao sobre funçao ?
Porque é uma função composta,você substitui a função no lugar do x,por isso fica dividindo.
blz obg
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