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

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

f (x) = x^{2} - 2 x^{3}

f (x) = - x^{2} + 10 x - 21

f (x) = \frac{3 - 3 x}{6 x - 1}

(\frac{1}{3}, - \frac{5}{4}), (\frac{3}{4}, - 4)

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