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

The domain of f(x)=(sqrt(3-x))/(x^2-2x) is x<0\lor 0<x<2\lor 2<x<= 3

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

domain

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

x < 0 or 0 < x < 2 or 2 < x \leq 3

Interval Notation

(- \infty, 0) \cup (0, 2) \cup (2, 3]

Solution steps

Find non-negative values for radicals:

x \leq 3

Find undefined (singularity) points:

x = 2, x = 0

Combine real regions and undefined points for final function domain

x < 0 or 0 < x < 2 or 2 < x \leq 3

\frac{1}{x ln ( x ^{2} - 1 )}

f (x) = 4 x - 2 ln (x)

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

(1 - \frac{3}{x})^{x}

f (x) = x + ln (x)

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