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

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

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

domain

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

- \frac{1}{2} < x \leq - \frac{1}{9} or x > \frac{2}{3}

Interval Notation

(- \frac{1}{2}, - \frac{1}{9}] \cup (\frac{2}{3}, \infty)

Solution steps

Find non-negative values for radicals:

- \frac{1}{2} < x \leq - \frac{1}{9} or x > \frac{2}{3}

Find undefined (singularity) points:

x = - \frac{1}{2}, x = \frac{2}{3}

Combine real regions and undefined points for final function domain

- \frac{1}{2} < x \leq - \frac{1}{9} or x > \frac{2}{3}

f (x) = \frac{8 x + 3}{- 5 - 5 x}

f (x) = \frac{7}{x - 5}

- 2 cos (\frac{1}{4}) (y - \frac{π}{2})

y = 3 x

\frac{x ^{2} - 25}{6 x + 1}

What is the domain of f(x)=sqrt(1/(2x+1)-3/(2-3x)) ?
The domain of f(x)=sqrt(1/(2x+1)-3/(2-3x)) is -1/2 <x<=-1/9 \lor x> 2/3