What is the domain of f(x)=(sqrt(x+7))/(-3x+10) ?

The domain of f(x)=(sqrt(x+7))/(-3x+10) is -7 10/3

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domain of f(x)=(sqrt(x+7))/(-3x+10)

domain

f (x) = \frac{x + 7}{- 3 x + 10}

- 7 \leq x < \frac{10}{3} or x > \frac{10}{3}

Interval Notation

[- 7, \frac{10}{3}) \cup (\frac{10}{3}, \infty)

Solution steps

Find non-negative values for radicals:

x \geq - 7

Find undefined (singularity) points:

x = \frac{10}{3}

Combine real regions and undefined points for final function domain

- 7 \leq x < \frac{10}{3} or x > \frac{10}{3}

What is the domain of f(x)=(sqrt(x+7))/(-3x+10) ?
The domain of f(x)=(sqrt(x+7))/(-3x+10) is -7<= x< 10/3 \lor x> 10/3