What is the domain of f(x)=sqrt((1-ln(x))/(2+ln(x))) ?

The domain of f(x)=sqrt((1-ln(x))/(2+ln(x))) is 1/(e^2)<x<= e

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domain of f(x)=sqrt((1-ln(x))/(2+ln(x)))

domain

f (x) = \frac{1 - ln ( x )}{2 + ln ( x )}

\frac{1}{e ^{2}} < x \leq e

Interval Notation

(\frac{1}{e ^{2}}, e]

Solution steps

Find non-negative values for radicals:

\frac{1}{e ^{2}} < x \leq e

Find undefined (singularity) points:

x = \frac{1}{e ^{2}}

Combine real regions and undefined points for final function domain

\frac{1}{e ^{2}} < x \leq e

f (x) = 8 + 7 x - 8

2 x^{2} + 3 x - 20

f (x) = x \cdot e^{x}

tan (x - \frac{π}{2})

f (x) = \frac{1}{( x - 1 ) ( x - 2 )}

What is the domain of f(x)=sqrt((1-ln(x))/(2+ln(x))) ?
The domain of f(x)=sqrt((1-ln(x))/(2+ln(x))) is 1/(e^2)<x<= e