determine o valor da função g(5),sabendo que f[g(x)]=3x² e que f(x)=3x=1
Celio:
Fabricia, é "f(x) = 3x + 1"? Não funcionou a tecla [shift] ?
Respostas
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Olá, Fabriciathaynar.
![f[g(x)]=3x^2\\\\
f(x)=3x+1\Rightarrow f[g(x)]=3g(x)+1\\\\
\text{Como }f[g(x)]=3x^2,\text{ ent\~ao:}\\\\
3g(x)+1=3x^2\Rightarrow 3g(x)=3x^2-1\Rightarrow g(x)=\frac{3x^2-1}3\Rightarrow \\\\ g(x)=x^2-\frac13\\\\
\text{Portanto: }\\g(5)=5^2-\frac13=25-\frac13=\frac{75-1}3=\boxed{\frac{74}3}](https://tex.z-dn.net/?f=f%5Bg%28x%29%5D%3D3x%5E2%5C%5C%5C%5C%0Af%28x%29%3D3x%2B1%5CRightarrow+f%5Bg%28x%29%5D%3D3g%28x%29%2B1%5C%5C%5C%5C%0A%5Ctext%7BComo+%7Df%5Bg%28x%29%5D%3D3x%5E2%2C%5Ctext%7B+ent%5C%7Eao%3A%7D%5C%5C%5C%5C%0A3g%28x%29%2B1%3D3x%5E2%5CRightarrow+3g%28x%29%3D3x%5E2-1%5CRightarrow+g%28x%29%3D%5Cfrac%7B3x%5E2-1%7D3%5CRightarrow+%5C%5C%5C%5C+g%28x%29%3Dx%5E2-%5Cfrac13%5C%5C%5C%5C%0A%5Ctext%7BPortanto%3A+%7D%5C%5Cg%285%29%3D5%5E2-%5Cfrac13%3D25-%5Cfrac13%3D%5Cfrac%7B75-1%7D3%3D%5Cboxed%7B%5Cfrac%7B74%7D3%7D "f[g(x)]=3x^2\\\\
f(x)=3x+1\Rightarrow f[g(x)]=3g(x)+1\\\\
\text{Como }f[g(x)]=3x^2,\text{ ent\~ao:}\\\\
3g(x)+1=3x^2\Rightarrow 3g(x)=3x^2-1\Rightarrow g(x)=\frac{3x^2-1}3\Rightarrow \\\\ g(x)=x^2-\frac13\\\\
\text{Portanto: }\\g(5)=5^2-\frac13=25-\frac13=\frac{75-1}3=\boxed{\frac{74}3}")
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