What is the domain of f(x)=sqrt((9-x)/(x-3)) ?

The domain of f(x)=sqrt((9-x)/(x-3)) is 3<x<= 9

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domain of f(x)=sqrt((9-x)/(x-3))

domain

f (x) = \frac{9 - x}{x - 3}

3 < x \leq 9

Interval Notation

(3, 9]

Solution steps

Find non-negative values for radicals:

3 < x \leq 9

Find undefined (singularity) points:

x = 3

Combine real regions and undefined points for final function domain

3 < x \leq 9

y = \frac{3 x + 4}{x ^{2} + 7 x + 12}

4 tan (2 x + \frac{π}{3}) - 1

4 x - 6, x = - 2

f (x) = sec^{\frac{1}{2}} (x)

\frac{x - 12}{5}

What is the domain of f(x)=sqrt((9-x)/(x-3)) ?
The domain of f(x)=sqrt((9-x)/(x-3)) is 3<x<= 9