What is the domain of f(x)=sqrt((21-2x)/(x-9)) ?

The domain of f(x)=sqrt((21-2x)/(x-9)) is 9<x<= 21/2

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domain of f(x)=sqrt((21-2x)/(x-9))

domain

9 < x \leq \frac{21}{2}

Interval Notation

(9, \frac{21}{2}]

Solution steps

Find non-negative values for radicals:

9 < x \leq \frac{21}{2}

Find undefined (singularity) points:

x = 9

Combine real regions and undefined points for final function domain

9 < x \leq \frac{21}{2}

What is the domain of f(x)=sqrt((21-2x)/(x-9)) ?
The domain of f(x)=sqrt((21-2x)/(x-9)) is 9<x<= 21/2