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

The domain of 1/(sqrt(2-3x)) is x< 2/3

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domain of 1/(sqrt(2-3x))

domain

\frac{1}{2 - 3 x}

x < \frac{2}{3}

Interval Notation

(- \infty, \frac{2}{3})

Solution steps

Find non-negative values for radicals:

x \leq \frac{2}{3}

Find undefined (singularity) points:

x = \frac{2}{3}

Combine real regions and undefined points for final function domain

x < \frac{2}{3}

3 x + 2 y = - 12

f (x) = \frac{x}{x ^{2} - 5 x - 6}

\frac{x - 6}{x + 6}

f (x) = 2 x (2 x^{2} + 8 x)

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