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

The domain of f(x)=sqrt((2x+1)/(x-2)) is x 2

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

domain

f (x) = \frac{2 x + 1}{x - 2}

x \leq - \frac{1}{2} or x > 2

Interval Notation

(- \infty, - \frac{1}{2}] \cup (2, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - \frac{1}{2} or x > 2

Find undefined (singularity) points:

x = 2

Combine real regions and undefined points for final function domain

x \leq - \frac{1}{2} or x > 2

- \frac{1}{2 ( 1 - x ) ^{\frac{5}{2}}}

3 x - 5 + 2 x + 1

f (x) = \frac{5 x + x ^{2}}{x ^{2} + x ^{3} - x + 1}

\frac{- 3 x}{x ^{4} - 3}

\frac{1}{x ^{2} + 10}

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