What is the domain of (sqrt(2x))/(3x-8) ?

The domain of (sqrt(2x))/(3x-8) is 0 8/3

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domain of (sqrt(2x))/(3x-8)

domain

\frac{2 x}{3 x - 8}

0 \leq x < \frac{8}{3} or x > \frac{8}{3}

Interval Notation

[0, \frac{8}{3}) \cup (\frac{8}{3}, \infty)

Solution steps

Find non-negative values for radicals:

x \geq 0

Find undefined (singularity) points:

x = \frac{8}{3}

Combine real regions and undefined points for final function domain

0 \leq x < \frac{8}{3} or x > \frac{8}{3}

f (x) = e^{x} (x^{2} + x) x - sin (x)

f (x) = 2 x^{2} + 6 x + 10

f (x) = \frac{x}{4 x - 3}

f (x) = 3 - 2 x^{5}

f (x) = x - 4

What is the domain of (sqrt(2x))/(3x-8) ?
The domain of (sqrt(2x))/(3x-8) is 0<= x< 8/3 \lor x> 8/3