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Anexos:
Soluções para a tarefa
Respondido por
2
Boa noite Marcelo!
Solução!
![f\left ( \frac{1}{x} \right )=-f(x)\\\\\\
x= \dfrac{1}{x}\\\\\\Vamos~~agora~~substituir~~na~~fuc\~ao.\\\\\\
\dfrac{1+x}{ \dfrac{x}{~~\dfrac{1}{x} -1} }+1 = -\dfrac{x+1}{x-1}\\\\\\\
\dfrac{1+x}{ \dfrac{x}{ \dfrac{1-x}{x} } } = -\dfrac{x+1}{x-1}\\\\\\\
\frac{1+x}{x} . \frac{x}{1-x} = -\dfrac{x+1}{x-1}\\\\\\
\frac{1+x}{1-x}= -\dfrac{x+1}{x-1}\\\\\\
Organizando!\\\\\\\
\frac{x+1}{-x+1}= -\dfrac{x+1}{x-1}\\\\\\
Multiplicando~~o~~denominador~~por~~-1\\\\\\](https://tex.z-dn.net/?f=f%5Cleft+%28+%5Cfrac%7B1%7D%7Bx%7D+%5Cright+%29%3D-f%28x%29%5C%5C%5C%5C%5C%5C%0Ax%3D+%5Cdfrac%7B1%7D%7Bx%7D%5C%5C%5C%5C%5C%5CVamos%7E%7Eagora%7E%7Esubstituir%7E%7Ena%7E%7Efuc%5C%7Eao.%5C%5C%5C%5C%5C%5C%0A%0A++%5Cdfrac%7B1%2Bx%7D%7B+%5Cdfrac%7Bx%7D%7B%7E%7E%5Cdfrac%7B1%7D%7Bx%7D+-1%7D+%7D%2B1+%3D+-%5Cdfrac%7Bx%2B1%7D%7Bx-1%7D%5C%5C%5C%5C%5C%5C%5C%0A++%5Cdfrac%7B1%2Bx%7D%7B+%5Cdfrac%7Bx%7D%7B+%5Cdfrac%7B1-x%7D%7Bx%7D+%7D+%7D++%3D+-%5Cdfrac%7Bx%2B1%7D%7Bx-1%7D%5C%5C%5C%5C%5C%5C%5C%0A+%5Cfrac%7B1%2Bx%7D%7Bx%7D+.+%5Cfrac%7Bx%7D%7B1-x%7D+%3D+-%5Cdfrac%7Bx%2B1%7D%7Bx-1%7D%5C%5C%5C%5C%5C%5C%0A%5Cfrac%7B1%2Bx%7D%7B1-x%7D%3D+-%5Cdfrac%7Bx%2B1%7D%7Bx-1%7D%5C%5C%5C%5C%5C%5C%0AOrganizando%21%5C%5C%5C%5C%5C%5C%5C%0A%5Cfrac%7Bx%2B1%7D%7B-x%2B1%7D%3D+-%5Cdfrac%7Bx%2B1%7D%7Bx-1%7D%5C%5C%5C%5C%5C%5C%0AMultiplicando%7E%7Eo%7E%7Edenominador%7E%7Epor%7E%7E-1%5C%5C%5C%5C%5C%5C%0A%0A%0A%0A++ "f\left ( \frac{1}{x} \right )=-f(x)\\\\\\
x= \dfrac{1}{x}\\\\\\Vamos~~agora~~substituir~~na~~fuc\~ao.\\\\\\
\dfrac{1+x}{ \dfrac{x}{~~\dfrac{1}{x} -1} }+1 = -\dfrac{x+1}{x-1}\\\\\\\
\dfrac{1+x}{ \dfrac{x}{ \dfrac{1-x}{x} } } = -\dfrac{x+1}{x-1}\\\\\\\
\frac{1+x}{x} . \frac{x}{1-x} = -\dfrac{x+1}{x-1}\\\\\\
\frac{1+x}{1-x}= -\dfrac{x+1}{x-1}\\\\\\
Organizando!\\\\\\\
\frac{x+1}{-x+1}= -\dfrac{x+1}{x-1}\\\\\\
Multiplicando~~o~~denominador~~por~~-1\\\\\\")
Exercício 2
![f(x)= \dfrac{x+1}{x-1} \\\\\\\
g(x)=2x+3\\\\\\
D(fog)-\{-1\}\\\\\\
fog=f(g)x)\\\\\\
fog = \dfrac{(2x+3)+1}{(2x+3)-1}\\\\\\
fog = \dfrac{2x+3+1}{2x+3-1}\\\\\\
fog = \dfrac{2x+4}{2x+2}\\\\\\
Simplificando!\\\\\\\\
fog = \dfrac{(x+2)}{(x+1)}\\\\\\
fog = \dfrac{(x+2)}{(x+1)}\\\\\\](https://tex.z-dn.net/?f=f%28x%29%3D+%5Cdfrac%7Bx%2B1%7D%7Bx-1%7D+%5C%5C%5C%5C%5C%5C%5C%0Ag%28x%29%3D2x%2B3%5C%5C%5C%5C%5C%5C%0AD%28fog%29-%5C%7B-1%5C%7D%5C%5C%5C%5C%5C%5C%0Afog%3Df%28g%29x%29%5C%5C%5C%5C%5C%5C%0Afog+%3D+%5Cdfrac%7B%282x%2B3%29%2B1%7D%7B%282x%2B3%29-1%7D%5C%5C%5C%5C%5C%5C%0Afog+%3D+%5Cdfrac%7B2x%2B3%2B1%7D%7B2x%2B3-1%7D%5C%5C%5C%5C%5C%5C%0Afog+%3D+%5Cdfrac%7B2x%2B4%7D%7B2x%2B2%7D%5C%5C%5C%5C%5C%5C%0ASimplificando%21%5C%5C%5C%5C%5C%5C%5C%5C%0Afog+%3D+%5Cdfrac%7B%28x%2B2%29%7D%7B%28x%2B1%29%7D%5C%5C%5C%5C%5C%5C%0Afog+%3D+%5Cdfrac%7B%28x%2B2%29%7D%7B%28x%2B1%29%7D%5C%5C%5C%5C%5C%5C%0A "f(x)= \dfrac{x+1}{x-1} \\\\\\\
g(x)=2x+3\\\\\\
D(fog)-\{-1\}\\\\\\
fog=f(g)x)\\\\\\
fog = \dfrac{(2x+3)+1}{(2x+3)-1}\\\\\\
fog = \dfrac{2x+3+1}{2x+3-1}\\\\\\
fog = \dfrac{2x+4}{2x+2}\\\\\\
Simplificando!\\\\\\\\
fog = \dfrac{(x+2)}{(x+1)}\\\\\\
fog = \dfrac{(x+2)}{(x+1)}\\\\\\")
![fog = \dfrac{(x+2)}{(x+1)}\\\\\
x+1 \neq 0\\\\\\
x \neq -1\\\\\\\\
Logo!\\\\\
Dominio~s\~ao~todos~os~reais~excluindo~~-1\\\\\
~~pois~~n\~ao~existe~~divis\~ao~por~~0\\\\\\
Resposta!\\\\\
\boxed{D(fog)=\mathbb{R}-\{-1\}}](https://tex.z-dn.net/?f=fog+%3D+%5Cdfrac%7B%28x%2B2%29%7D%7B%28x%2B1%29%7D%5C%5C%5C%5C%5C%0Ax%2B1+%5Cneq+0%5C%5C%5C%5C%5C%5C%0Ax+%5Cneq+-1%5C%5C%5C%5C%5C%5C%5C%5C%0ALogo%21%5C%5C%5C%5C%5C%0ADominio%7Es%5C%7Eao%7Etodos%7Eos%7Ereais%7Eexcluindo%7E%7E-1%5C%5C%5C%5C%5C%0A%7E%7Epois%7E%7En%5C%7Eao%7Eexiste%7E%7Edivis%5C%7Eao%7Epor%7E%7E0%5C%5C%5C%5C%5C%5C%0AResposta%21%5C%5C%5C%5C%5C%0A%5Cboxed%7BD%28fog%29%3D%5Cmathbb%7BR%7D-%5C%7B-1%5C%7D%7D "fog = \dfrac{(x+2)}{(x+1)}\\\\\
x+1 \neq 0\\\\\\
x \neq -1\\\\\\\\
Logo!\\\\\
Dominio~s\~ao~todos~os~reais~excluindo~~-1\\\\\
~~pois~~n\~ao~existe~~divis\~ao~por~~0\\\\\\
Resposta!\\\\\
\boxed{D(fog)=\mathbb{R}-\{-1\}}")
Boa noite!
Bons estudos!
Solução!
Exercício 2
Boa noite!
Bons estudos!
MarceloDani:
bah, não consegui visualizar, mano
Você esta no celular?
Sim
Pronto, abri mo computador
Valeu brother! Tmjo. Não ia me ligar.
No celular você não consegue ver a escrita no latex!
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