What is the domain of f(x)=(sqrt(6+x))/(-8+3x) ?

The domain of f(x)=(sqrt(6+x))/(-8+3x) is -6 8/3

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domain of f(x)=(sqrt(6+x))/(-8+3x)

domain

f (x) = \frac{6 + x}{- 8 + 3 x}

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

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \geq - 6

Find undefined (singularity) points:

x = \frac{8}{3}

Combine real regions and undefined points for final function domain

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

\frac{10 x}{3 x ^{2} + 8}

f (x) = 7 - 2 x

y = \frac{- 9 x ^{2}}{( x - 2 ) ( x + 8 )}

f (x) = - x + 1, x \leq 1

f (x) = x^{2} + 10 x + 24

What is the domain of f(x)=(sqrt(6+x))/(-8+3x) ?
The domain of f(x)=(sqrt(6+x))/(-8+3x) is -6<= x< 8/3 \lor x> 8/3