What is the domain of ((-x+sqrt((9x^2+8x))))/(2x) ?

The domain of ((-x+sqrt((9x^2+8x))))/(2x) is x 0

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domain of ((-x+sqrt((9x^2+8x))))/(2x)

domain

\frac{( - x + ( 9 x ^{2} + 8 x ) )}{2 x}

x \leq - \frac{8}{9} or x > 0

Interval Notation

Solution steps

Find non-negative values for radicals:

x \leq - \frac{8}{9} or x \geq 0

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

x \leq - \frac{8}{9} or x > 0

2 (π) (r^{2}) + 12 (π) (r)

x^{3} + 2 x + 5

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

f (x) = \frac{x - 4}{x - 1 + 2}

f (x) = 5^{2 x - 1} - 2

What is the domain of ((-x+sqrt((9x^2+8x))))/(2x) ?
The domain of ((-x+sqrt((9x^2+8x))))/(2x) is x<=-8/9 \lor x>0