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

The domain of f(x)=ln((x^2-2)/(2x-1)) is -sqrt(2) sqrt(2)

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domain of f(x)=ln((x^2-2)/(2x-1))

domain

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

- 2 < x < \frac{1}{2} or x > 2

Interval Notation

(- 2, \frac{1}{2}) \cup (2, \infty)

Solution steps

Find positive values for logs:

- 2 < x < \frac{1}{2} or x > 2

Find undefined (singularity) points:

x = \frac{1}{2}

Combine real regions and undefined points for final function domain

- 2 < x < \frac{1}{2} or x > 2

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