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# What is f(x) = int 1/(x-4)  if f(2)=1 ?

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#### Explanation

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#### Explanation:

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Jun 21, 2018

$f \left(x\right) = \ln | x - 4 | + \ln \left(\frac{e}{2}\right)$

OR

$f \left(x\right) = \ln | x - 4 | + 1 - \ln 2$

#### Explanation:

Here,

$f \left(x\right) = \int \frac{1}{x - 4} \mathrm{dx}$

$f \left(x\right) = \ln | x - 4 | + c \ldots . \to \left(1\right)$

Given that ,

$f \left(2\right) = 1$

$\implies \ln | 2 - 4 | + c = 1$

$\implies \ln | - 2 | + c = 1$

$\implies c = 1 - \ln 2$

$\implies c = \ln e - \ln 2. . . \to \left[\because \ln e = 1\right]$

$\implies c = \ln \left(\frac{e}{2}\right)$

Subst. $c = \ln \left(\frac{e}{2}\right)$ , into $\left(1\right)$

$f \left(x\right) = \ln | x - 4 | + \ln \left(\frac{e}{2}\right)$

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