What is the domain of f(x)=sqrt((x-3)/(x-5)) ?

The domain of f(x)=sqrt((x-3)/(x-5)) is x 5

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domain of f(x)=sqrt((x-3)/(x-5))

domain

f (x) = \frac{x - 3}{x - 5}

x \leq 3 or x > 5

Interval Notation

(- \infty, 3] \cup (5, \infty)

Solution steps

Find non-negative values for radicals:

x \leq 3 or x > 5

Find undefined (singularity) points:

x = 5

Combine real regions and undefined points for final function domain

x \leq 3 or x > 5

What is the domain of f(x)=sqrt((x-3)/(x-5)) ?
The domain of f(x)=sqrt((x-3)/(x-5)) is x<= 3\lor x>5