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

The domain of f(x)=sqrt(x/(2-3x)) is 0<= x< 2/3

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

domain

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

0 \leq x < \frac{2}{3}

Interval Notation

[0, \frac{2}{3})

Solution steps

Find non-negative values for radicals:

0 \leq x < \frac{2}{3}

Find undefined (singularity) points:

x = \frac{2}{3}

Combine real regions and undefined points for final function domain

0 \leq x < \frac{2}{3}

f (x) = ln (x - 20)

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

\frac{3 x ^{2} + 5 x - 3}{8 x ^{2}}

f (x) = 25 + 5^{x}

lo g_{10} (13 - x)

What is the domain of f(x)=sqrt(x/(2-3x)) ?
The domain of f(x)=sqrt(x/(2-3x)) is 0<= x< 2/3