What is the domain of 1/(2xsqrt(3+ln(x))) ?

The domain of 1/(2xsqrt(3+ln(x))) is x> 1/(e^3)

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domain of 1/(2xsqrt(3+ln(x)))

domain

\frac{1}{2 x 3 + ln ( x )}

x > \frac{1}{e ^{3}}

Interval Notation

(\frac{1}{e ^{3}}, \infty)

Solution steps

Find non-negative values for radicals:

x \geq \frac{1}{e ^{3}}

Find undefined (singularity) points:

x = \frac{1}{e ^{3}}

Combine real regions and undefined points for final function domain

x > \frac{1}{e ^{3}}

\frac{x ^{2} + 5 x + 6}{x ^{2} - 4}

f (x) = 3 - 2 x - 4

- 3 x + 9

f (x) = \frac{2 x + 3}{3 x - 2}

f (x) = \frac{10 - 3 x - x ^{2}}{∣ x - 2 ∣}

What is the domain of 1/(2xsqrt(3+ln(x))) ?
The domain of 1/(2xsqrt(3+ln(x))) is x> 1/(e^3)