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

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

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

domain

\frac{1}{2 x 2 + ln ( x )}

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}}

\frac{3 x - 2}{x ^{2} - 3 x - 4}

f (x) = \frac{5}{3 x - 8}

- \frac{2}{3} (x - 4) - 2

\frac{x + 13}{x ^{4} + x ^{3} - 3 x ^{2} - 3 x}

f (x) = 7 x^{2} - 28 x - 35

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