What is the domain of f(x)=sqrt((x-1)/(x-3)) ?

The domain of f(x)=sqrt((x-1)/(x-3)) is x 3

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domain of f(x)=sqrt((x-1)/(x-3))

domain

f (x) = \frac{x - 1}{x - 3}

x \leq 1 or x > 3

Interval Notation

(- \infty, 1] \cup (3, \infty)

Solution steps

Find non-negative values for radicals:

x \leq 1 or x > 3

Find undefined (singularity) points:

x = 3

Combine real regions and undefined points for final function domain

x \leq 1 or x > 3

f (x) = \frac{3 x ^{2} - 2 x - 1}{x ^{2} + 3 x - 10}

sec (3 x)

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

f (x) = 1 - 1

- \frac{1 - x}{1 + x}

What is the domain of f(x)=sqrt((x-1)/(x-3)) ?
The domain of f(x)=sqrt((x-1)/(x-3)) is x<= 1\lor x>3