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

The domain of f(x)=(sqrt(1-ln(x)))/(1-x^2) is 0<x<1\lor 1<x<= e

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

domain

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

0 < x < 1 or 1 < x \leq e

Interval Notation

(0, 1) \cup (1, e]

Solution steps

Find non-negative values for radicals:

0 < x \leq e

Find undefined (singularity) points:

x = 1, x = - 1

Combine real regions and undefined points for final function domain

0 < x < 1 or 1 < x \leq e

f (x) = \frac{10}{x ^{2} + 4}

f (x) = \frac{x ^{2} + x - 20}{x ^{2} - 14 x + 48}

\frac{2}{x + 7}

f (x) = lo g_{\frac{1}{2}} (lo g_{2} (x - 3))

\frac{x - 2}{x ^{2} - 2 x}

What is the domain of f(x)=(sqrt(1-ln(x)))/(1-x^2) ?
The domain of f(x)=(sqrt(1-ln(x)))/(1-x^2) is 0<x<1\lor 1<x<= e