What is the domain of f(x)= x/(sqrt(4-ln^2(x))) ?

The domain of f(x)= x/(sqrt(4-ln^2(x))) is 1/(e^2)<x<e^2

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domain of f(x)= x/(sqrt(4-ln^2(x)))

domain

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

Interval Notation

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

Solution steps

Find non-negative values for radicals:

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

Find undefined (singularity) points:

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

Combine real regions and undefined points for final function domain

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

What is the domain of f(x)= x/(sqrt(4-ln^2(x))) ?
The domain of f(x)= x/(sqrt(4-ln^2(x))) is 1/(e^2)<x<e^2