What is the domain of f(x)=ln(sqrt(((x-5))/(x-1))) ?

The domain of f(x)=ln(sqrt(((x-5))/(x-1))) is x 5

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domain of f(x)=ln(sqrt(((x-5))/(x-1)))

domain

f (x) = ln (\frac{( x - 5 )}{x - 1})

x < 1 or x > 5

Interval Notation

(- \infty, 1) \cup (5, \infty)

Solution steps

Find positive values for logs:

x < 1 or x > 5

Find undefined (singularity) points:

x = 1

Combine real regions and undefined points for final function domain

x < 1 or x > 5

\frac{x ^{2} - x}{x ^{2} - 8 x + 7}

(- 5, 4), (3, - 8)

f (x) = \frac{x - 2}{3 x + 7}

f (x) = 2 (x + 5)^{\frac{1}{2}}

\frac{2 x + 7}{3 x - 17}

What is the domain of f(x)=ln(sqrt(((x-5))/(x-1))) ?
The domain of f(x)=ln(sqrt(((x-5))/(x-1))) is x<1\lor x>5