na função f(x)=log2(x+1)-½ quanto vale f(3)+3f(0)?
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Acho que a equação é essa: ![f(x)= log_{2}[(x+1)-\frac{1}{2}]](https://tex.z-dn.net/?f=f%28x%29%3D+log_%7B2%7D%5B%28x%2B1%29-%5Cfrac%7B1%7D%7B2%7D%5D "f(x)= log_{2}[(x+1)-\frac{1}{2}]")
Vamos substituir os valores:
![f(x)= log_{2}[(x+1)-\frac{1}{2}] \\ \\ x=3\\ \\f(3)= log_{2}[(3+1)-\frac{1}{2}] \\ \\
f(3)= log_{2}[(4)-\frac{1}{2}] \\ \\ f(3)= log_{2}[\frac{8}{2}-\frac{1}{2}] \\ \\
f(3)= log_{2}[\frac{7}{2}] \\ \\ propriedade \\ \\
f(3)= log_{2}[7] -log_{2}[{2}]\\ \\f(3)= log_{2}[7] - 1](https://tex.z-dn.net/?f=f%28x%29%3D+log_%7B2%7D%5B%28x%2B1%29-%5Cfrac%7B1%7D%7B2%7D%5D+%5C%5C+%5C%5C+x%3D3%5C%5C+%5C%5Cf%283%29%3D+log_%7B2%7D%5B%283%2B1%29-%5Cfrac%7B1%7D%7B2%7D%5D+%5C%5C+%5C%5C+%0Af%283%29%3D+log_%7B2%7D%5B%284%29-%5Cfrac%7B1%7D%7B2%7D%5D+%5C%5C+%5C%5C+f%283%29%3D+log_%7B2%7D%5B%5Cfrac%7B8%7D%7B2%7D-%5Cfrac%7B1%7D%7B2%7D%5D+%5C%5C+%5C%5C+%0Af%283%29%3D+log_%7B2%7D%5B%5Cfrac%7B7%7D%7B2%7D%5D+%5C%5C+%5C%5C+propriedade+%5C%5C+%5C%5C+%0Af%283%29%3D+log_%7B2%7D%5B7%5D+-log_%7B2%7D%5B%7B2%7D%5D%5C%5C+%5C%5Cf%283%29%3D+log_%7B2%7D%5B7%5D+-+1+ "f(x)= log_{2}[(x+1)-\frac{1}{2}] \\ \\ x=3\\ \\f(3)= log_{2}[(3+1)-\frac{1}{2}] \\ \\
f(3)= log_{2}[(4)-\frac{1}{2}] \\ \\ f(3)= log_{2}[\frac{8}{2}-\frac{1}{2}] \\ \\
f(3)= log_{2}[\frac{7}{2}] \\ \\ propriedade \\ \\
f(3)= log_{2}[7] -log_{2}[{2}]\\ \\f(3)= log_{2}[7] - 1")
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![f(x)= log_{2}[(x+1)-\frac{1}{2}] \\ \\ x=0\\ \\f(0)= log_{2}[(0+1)-\frac{1}{2}] \\ \\
f(0)= log_{2}[\frac{2}{2}-\frac{1}{2}] \\ \\f(0)= log_{2}[\frac{1}{2}] \\ \\ propriedade \\ \\
f(0)= log_{2}1-log_{2}2 \\ \\ f(0)=0-1 \\ \\ f(0) = 1 \\ \\ multiplicando \\ \\
3*f(0)=3*1=3](https://tex.z-dn.net/?f=f%28x%29%3D+log_%7B2%7D%5B%28x%2B1%29-%5Cfrac%7B1%7D%7B2%7D%5D+%5C%5C+%5C%5C+x%3D0%5C%5C+%5C%5Cf%280%29%3D+log_%7B2%7D%5B%280%2B1%29-%5Cfrac%7B1%7D%7B2%7D%5D+%5C%5C+%5C%5C+%0Af%280%29%3D+log_%7B2%7D%5B%5Cfrac%7B2%7D%7B2%7D-%5Cfrac%7B1%7D%7B2%7D%5D++%5C%5C+%5C%5Cf%280%29%3D+log_%7B2%7D%5B%5Cfrac%7B1%7D%7B2%7D%5D++%5C%5C+%5C%5C+propriedade+%5C%5C+%5C%5C%0Af%280%29%3D+log_%7B2%7D1-log_%7B2%7D2++%5C%5C+%5C%5C+f%280%29%3D0-1+%5C%5C+%5C%5C+f%280%29+%3D+1+%5C%5C+%5C%5C+multiplicando+%5C%5C+%5C%5C+%0A3%2Af%280%29%3D3%2A1%3D3 "f(x)= log_{2}[(x+1)-\frac{1}{2}] \\ \\ x=0\\ \\f(0)= log_{2}[(0+1)-\frac{1}{2}] \\ \\
f(0)= log_{2}[\frac{2}{2}-\frac{1}{2}] \\ \\f(0)= log_{2}[\frac{1}{2}] \\ \\ propriedade \\ \\
f(0)= log_{2}1-log_{2}2 \\ \\ f(0)=0-1 \\ \\ f(0) = 1 \\ \\ multiplicando \\ \\
3*f(0)=3*1=3")
Somando os resultados:
![y=f(3)+3*f(0) \\ \\ y=(log_{2}[7] - 1)+3 \\ \\ y=log_{2}(7) +2](https://tex.z-dn.net/?f=y%3Df%283%29%2B3%2Af%280%29+%5C%5C+%5C%5C+y%3D%28log_%7B2%7D%5B7%5D+-+1%29%2B3+%5C%5C+%5C%5C+y%3Dlog_%7B2%7D%287%29+%2B2 "y=f(3)+3*f(0) \\ \\ y=(log_{2}[7] - 1)+3 \\ \\ y=log_{2}(7) +2")
Vamos substituir os valores:
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Somando os resultados:
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