What is the domain of f(x)=sqrt((2x+3)/(x-9)) ?

The domain of f(x)=sqrt((2x+3)/(x-9)) is x 9

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domain of f(x)=sqrt((2x+3)/(x-9))

domain

f (x) = \frac{2 x + 3}{x - 9}

x \leq - \frac{3}{2} or x > 9

Interval Notation

(- \infty, - \frac{3}{2}] \cup (9, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - \frac{3}{2} or x > 9

Find undefined (singularity) points:

x = 9

Combine real regions and undefined points for final function domain

x \leq - \frac{3}{2} or x > 9

What is the domain of f(x)=sqrt((2x+3)/(x-9)) ?
The domain of f(x)=sqrt((2x+3)/(x-9)) is x<=-3/2 \lor x>9