What is the domain of f(x)=ln(sqrt(((x-9))/(x-3))) ?

The domain of f(x)=ln(sqrt(((x-9))/(x-3))) is x 9

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domain of f(x)=ln(sqrt(((x-9))/(x-3)))

domain

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

x < 3 or x > 9

Interval Notation

(- \infty, 3) \cup (9, \infty)

Solution steps

Find positive values for logs:

x < 3 or x > 9

Find undefined (singularity) points:

x = 3

Combine real regions and undefined points for final function domain

x < 3 or x > 9

x e^{x}

y (θ) = sin (θ + \frac{π}{2})

\frac{9 - x ^{2}}{x + 1}

f (x) = - \frac{( 1 )}{2 7 - x}

x + 8 - x

What is the domain of f(x)=ln(sqrt(((x-9))/(x-3))) ?
The domain of f(x)=ln(sqrt(((x-9))/(x-3))) is x<3\lor x>9