What is the domain of f(x)=sqrt((x^2-25)/(x^2-3x)) ?

The domain of f(x)=sqrt((x^2-25)/(x^2-3x)) is x = 5

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domain of f(x)=sqrt((x^2-25)/(x^2-3x))

domain

f (x) = \frac{x ^{2} - 25}{x ^{2} - 3 x}

x \leq - 5 or 0 < x < 3 or x \geq 5

Interval Notation

(- \infty, - 5] \cup (0, 3) \cup [5, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 5 or 0 < x < 3 or x \geq 5

Find undefined (singularity) points:

x = 3, x = 0

Combine real regions and undefined points for final function domain

x \leq - 5 or 0 < x < 3 or x \geq 5

f (x) = - x - 3 + 4

f (x) = \frac{1 - ln ( x )}{1 + ln ( x )}

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

f (x) = \frac{3 x - 2}{x + 6}

f (x) = 2 - 2 ln (x)

What is the domain of f(x)=sqrt((x^2-25)/(x^2-3x)) ?
The domain of f(x)=sqrt((x^2-25)/(x^2-3x)) is x<=-5\lor 0<x<3\lor x>= 5