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

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

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

domain

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

x \leq 2 or x > 3

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \leq 2 or x > 3

Find undefined (singularity) points:

x = 3

Combine real regions and undefined points for final function domain

x \leq 2 or x > 3

f (x) = \frac{1}{1 - lo g _{10} ( x )}

f (x) = x^{2} - 8 x + 21

x^{2} - 19

x^{10}

f (x) = \frac{x - 4}{x ^{2} + x - 20}

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