determine o valor da função g (5) sabendo que f [g(x)]=3x²+2 e que f (x)=3x-1
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Olá, Jander.
![f[g(x)]=3x^2+2\\\\f(x)=3x-1\Rightarrow f[g(x)]=3g(x)-1\\\\\text{Como }f[g(x)]=3x^2+2,\text{ ent\~ao:}\\\\3g(x)-1=3x^2+2\Rightarrow 3g(x)=3x^2+3\Rightarrow g(x)=\frac{3x^2+3}3\Rightarrow \\\\ g(x)=x^2+1\\\\\text{Portanto: }\\g(5)=5^2+1=25+1=\boxed{26}](https://tex.z-dn.net/?f=f%5Bg%28x%29%5D%3D3x%5E2%2B2%5C%5C%5C%5Cf%28x%29%3D3x-1%5CRightarrow+f%5Bg%28x%29%5D%3D3g%28x%29-1%5C%5C%5C%5C%5Ctext%7BComo+%7Df%5Bg%28x%29%5D%3D3x%5E2%2B2%2C%5Ctext%7B+ent%5C%7Eao%3A%7D%5C%5C%5C%5C3g%28x%29-1%3D3x%5E2%2B2%5CRightarrow+3g%28x%29%3D3x%5E2%2B3%5CRightarrow+g%28x%29%3D%5Cfrac%7B3x%5E2%2B3%7D3%5CRightarrow+%5C%5C%5C%5C+g%28x%29%3Dx%5E2%2B1%5C%5C%5C%5C%5Ctext%7BPortanto%3A+%7D%5C%5Cg%285%29%3D5%5E2%2B1%3D25%2B1%3D%5Cboxed%7B26%7D "f[g(x)]=3x^2+2\\\\f(x)=3x-1\Rightarrow f[g(x)]=3g(x)-1\\\\\text{Como }f[g(x)]=3x^2+2,\text{ ent\~ao:}\\\\3g(x)-1=3x^2+2\Rightarrow 3g(x)=3x^2+3\Rightarrow g(x)=\frac{3x^2+3}3\Rightarrow \\\\ g(x)=x^2+1\\\\\text{Portanto: }\\g(5)=5^2+1=25+1=\boxed{26}")
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