What is the domain of f(x)=sqrt(((x-2)/(x-3)))+5 ?

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

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domain of f(x)=sqrt(((x-2)/(x-3)))+5

domain

f (x) = (\frac{x - 2}{x - 3}) + 5

x \leq 2 or x > 3

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}{9 - t ^{2}}

(150, 147.9), (165, 163.4)

f (x) = - \frac{194}{63} x + \frac{6133}{6300}

7 - x

f (x) = 64 x^{2}

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