What is the domain of f(x)=sqrt(3-2*1/(x-2)) ?

The domain of f(x)=sqrt(3-2*1/(x-2)) is x = 8/3

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domain of f(x)=sqrt(3-2*1/(x-2))

domain

x < 2 or x \geq \frac{8}{3}

Interval Notation

(- \infty, 2) \cup [\frac{8}{3}, \infty)

Solution steps

Find non-negative values for radicals:

x < 2 or x \geq \frac{8}{3}

Find undefined (singularity) points:

x = 2

Combine real regions and undefined points for final function domain

x < 2 or x \geq \frac{8}{3}

What is the domain of f(x)=sqrt(3-2*1/(x-2)) ?
The domain of f(x)=sqrt(3-2*1/(x-2)) is x<2\lor x>= 8/3