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

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

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

domain

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

Interval Notation

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

Solution steps

Find non-negative values for radicals:

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

Find undefined (singularity) points:

x = 2

Combine real regions and undefined points for final function domain

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

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