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12) f(x)=ln((2+x)/(x-3)) ; 13) f(x)=lnvert (2x+3)/(x-5)vert

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12) f(x)=ln((2+x)/(x-3)) ; 13) f(x)=lnvert (2x+3)/(x-5)vert

12) f(x)=ln((2+x)/(x-3)) ; 13) f(x)=lnvert (2x+3)/(x-5)vert

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JanaíraMestre · Tutor por 5 anos

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12) The function $f(x)=ln(\frac {2+x}{x-3})$ is a logarithmic function with base $e$. The domain of this function is all real numbers except $x=3$, because the argument of the logarithm, $\frac {2+x}{x-3}$, must be greater than zero. Therefore, the correct answer is: The domain of $f(x)$ is all real numbers except $x=3$.<br /><br />13) The function $f(x)=ln\vert \frac {2x+3}{x-5}\vert $ is also a logarithmic function with base $e$. The domain of this function is all real numbers except $x=5$, because the argument of the logarithm, $\frac {2x+3}{x-5}$, must be greater than zero. Therefore, the correct answer is: The domain of $f(x)$ is all real numbers except $x=5$.
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