Para quais valores de f( x)a função exponencial f=(K+2)^x é descrescente ?
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Boa noite!
Solução!
Pela definição de função exponencial a curva e decrescente quado temos a seguinte condição!
![f(x)=k^{x} \\\\\\\
0\ \textless \ k\ \textless \ 1\\\\\\\\\
Logo!\\\\\\\\
f(x)=(k+2)^{x}\\\\\\\
Usando ~~o ~~mesmo~~ raciocinio~~colocado ~~acima! \\\\\\\
0\ \textless \ k+2\ \textless \ 1\\\\\entao\\\\\
k+2\ \textgreater \ 0\\\\\
k=-2\\\\\\
k+2\ \textless \ 1\\\\\
k\ \textless \ 1-2\\\\\
k\ \textless \ -1\\\\\\\
Concluimos~~ entao~~ que~~ K~~ pertece ~~ao~~ intervalo~~ aberto!\\\\\\\\
]-2,-1[](https://tex.z-dn.net/?f=f%28x%29%3Dk%5E%7Bx%7D+%5C%5C%5C%5C%5C%5C%5C%0A0%5C+%5Ctextless+%5C+k%5C+%5Ctextless+%5C+1%5C%5C%5C%5C%5C%5C%5C%5C%5C%0ALogo%21%5C%5C%5C%5C%5C%5C%5C%5C%0Af%28x%29%3D%28k%2B2%29%5E%7Bx%7D%5C%5C%5C%5C%5C%5C%5C%0AUsando+%7E%7Eo+%7E%7Emesmo%7E%7E+raciocinio%7E%7Ecolocado+%7E%7Eacima%21+%5C%5C%5C%5C%5C%5C%5C%0A0%5C+%5Ctextless+%5C+k%2B2%5C+%5Ctextless+%5C+1%5C%5C%5C%5C%5Centao%5C%5C%5C%5C%5C%0Ak%2B2%5C+%5Ctextgreater+%5C+0%5C%5C%5C%5C%5C%0Ak%3D-2%5C%5C%5C%5C%5C%5C%0Ak%2B2%5C+%5Ctextless+%5C+1%5C%5C%5C%5C%5C%0Ak%5C+%5Ctextless+%5C+1-2%5C%5C%5C%5C%5C%0Ak%5C+%5Ctextless+%5C+-1%5C%5C%5C%5C%5C%5C%5C%0AConcluimos%7E%7E+entao%7E%7E+que%7E%7E+K%7E%7E+pertece+%7E%7Eao%7E%7E+intervalo%7E%7E+aberto%21%5C%5C%5C%5C%5C%5C%5C%5C%0A%5D-2%2C-1%5B "f(x)=k^{x} \\\\\\\
0\ \textless \ k\ \textless \ 1\\\\\\\\\
Logo!\\\\\\\\
f(x)=(k+2)^{x}\\\\\\\
Usando ~~o ~~mesmo~~ raciocinio~~colocado ~~acima! \\\\\\\
0\ \textless \ k+2\ \textless \ 1\\\\\entao\\\\\
k+2\ \textgreater \ 0\\\\\
k=-2\\\\\\
k+2\ \textless \ 1\\\\\
k\ \textless \ 1-2\\\\\
k\ \textless \ -1\\\\\\\
Concluimos~~ entao~~ que~~ K~~ pertece ~~ao~~ intervalo~~ aberto!\\\\\\\\
]-2,-1[")
Boa noite!
Bons estudos!
Solução!
Pela definição de função exponencial a curva e decrescente quado temos a seguinte condição!
Boa noite!
Bons estudos!
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