What is the domain of f(x)=sqrt(2-(x-1)/(x-3)) ?

The domain of f(x)=sqrt(2-(x-1)/(x-3)) is x = 5

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domain of f(x)=sqrt(2-(x-1)/(x-3))

domain

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

x < 3 or x \geq 5

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x < 3 or x \geq 5

Find undefined (singularity) points:

x = 3

Combine real regions and undefined points for final function domain

x < 3 or x \geq 5

f (x) = \frac{2}{x - 5}

f (x) = \frac{13 x + 12}{23 x - 12}

y = x^{2} - 4 x + 5

2 x - 3 + \frac{5 x + 5}{x ^{2} - 1}

f (x) = \frac{5}{x + 2}

What is the domain of f(x)=sqrt(2-(x-1)/(x-3)) ?
The domain of f(x)=sqrt(2-(x-1)/(x-3)) is x<3\lor x>= 5