What is the domain of f(x)=(1-ln(x))/(1+ln(x)) ?

The domain of f(x)=(1-ln(x))/(1+ln(x)) is 0 1/e

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domain of f(x)=(1-ln(x))/(1+ln(x))

domain

f (x) = \frac{1 - ln ( x )}{1 + ln ( x )}

0 < x < \frac{1}{e} or x > \frac{1}{e}

Interval Notation

(0, \frac{1}{e}) \cup (\frac{1}{e}, \infty)

Solution steps

Find positive values for logs:

x > 0

Find undefined (singularity) points:

x = \frac{1}{e}

Combine real regions and undefined points for final function domain

0 < x < \frac{1}{e} or x > \frac{1}{e}

f (x) = \frac{t ^{2} + 7}{t}

f (x) = \frac{3 x - 2}{x + 6}

f (x) = 2 - 2 ln (x)

\frac{1}{( x + 5 ) ^{2}}

2 (x - 2) + 10

What is the domain of f(x)=(1-ln(x))/(1+ln(x)) ?
The domain of f(x)=(1-ln(x))/(1+ln(x)) is 0<x< 1/e \lor x> 1/e