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

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

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

domain

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

x \leq - 3 or x > 2

Interval Notation

(- \infty, - 3] \cup (2, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 3 or x > 2

Find undefined (singularity) points:

x = 2

Combine real regions and undefined points for final function domain

x \leq - 3 or x > 2

\frac{x ^{2} - 11 x + 18}{x ^{2} + 2 x - 8}

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

f (x) = \frac{5 x}{x ^{2} + 81}

7 x^{2} - 7 x

y = - \frac{1}{x}

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