What is the domain of f(x)=(sqrt(x+2))/(6x^2+x-2) ?

The domain of f(x)=(sqrt(x+2))/(6x^2+x-2) is -2 1/2

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domain of f(x)=(sqrt(x+2))/(6x^2+x-2)

domain

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

- 2 \leq x < - \frac{2}{3} or - \frac{2}{3} < x < \frac{1}{2} or x > \frac{1}{2}

Interval Notation

[- 2, - \frac{2}{3}) \cup (- \frac{2}{3}, \frac{1}{2}) \cup (\frac{1}{2}, \infty)

Solution steps

Find non-negative values for radicals:

x \geq - 2

Find undefined (singularity) points:

x = \frac{1}{2}, x = - \frac{2}{3}

Combine real regions and undefined points for final function domain

- 2 \leq x < - \frac{2}{3} or - \frac{2}{3} < x < \frac{1}{2} or x > \frac{1}{2}

What is the domain of f(x)=(sqrt(x+2))/(6x^2+x-2) ?
The domain of f(x)=(sqrt(x+2))/(6x^2+x-2) is -2<= x<-2/3 \lor-2/3 <x< 1/2 \lor x> 1/2