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

The domain of f(x)= 1/(x(ln(x)+2)) is 0 1/(e^2)

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

domain

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

0 < x < \frac{1}{e ^{2}} or x > \frac{1}{e ^{2}}

Interval Notation

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

Solution steps

Find positive values for logs:

x > 0

Find undefined (singularity) points:

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

Combine real regions and undefined points for final function domain

0 < x < \frac{1}{e ^{2}} or x > \frac{1}{e ^{2}}

f (x) = \frac{12 - 3 x ^{2}}{x - 3}

f (x) = 3 x (2 - x)

5 x - 2 x^{2} - x - 2

x^{2} + 11 x + 24

lo g_{10} (x^{4})

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