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

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

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

domain

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

- 3 \leq x < 3 or x > 3

Interval Notation

[- 3, 3) \cup (3, \infty)

Solution steps

Find non-negative values for radicals:

x \geq - 3

Find undefined (singularity) points:

x = 3

Combine real regions and undefined points for final function domain

- 3 \leq x < 3 or x > 3

- \frac{1}{x + 3}

f (x) = \frac{x ( x + 8 )}{9 ( x - 5 )}

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

\frac{5 x - 7}{x + 8}

\frac{x ^{2} - 9}{4 x + 8}

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