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

The domain of f(x)= 1/x-ln(x) is x>0

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domain of f(x)= 1/x-ln(x)

domain

f (x) = \frac{1}{x} - ln (x)

x > 0

Interval Notation

(0, \infty)

Solution steps

Find positive values for logs:

x > 0

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

x > 0

ln (- x^{2} + 5 x + 1)

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

f (x) = \frac{x - 3}{x ^{2} - 9}

4 3 x + 8 + 4

ln (- x^{2} + 5 x + 3)