What is the domain of f(x)=(sqrt(x+8))/(3x-8) ?

The domain of f(x)=(sqrt(x+8))/(3x-8) is -8 8/3

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domain of f(x)=(sqrt(x+8))/(3x-8)

domain

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

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

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \geq - 8

Find undefined (singularity) points:

x = \frac{8}{3}

Combine real regions and undefined points for final function domain

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

(20, 0), (30, 1)

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

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

f (x) = \frac{x ^{2}}{9 - x}

\frac{( x + 3 )}{( x ^{2} + 12 x + 27 )}

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