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

The domain of f(x)= 1/(2xsqrt(2+ln(x))) is x> 1/(e^2)

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

domain

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

Interval Notation

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

Solution steps

Find non-negative values for radicals:

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

Find undefined (singularity) points:

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

Combine real regions and undefined points for final function domain

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

What is the domain of f(x)= 1/(2xsqrt(2+ln(x))) ?
The domain of f(x)= 1/(2xsqrt(2+ln(x))) is x> 1/(e^2)