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

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

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

domain

y = \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) = lo g_{6} (x^{2} - 16)

f (x) = ln (x^{2} - 4 x)

lo g_{3} (\frac{x + 1}{x - 5})

lo g_{10} (x^{2} - 4)

- \frac{1}{x ^{2} + 6 x - 7}

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