What is the domain of sqrt(x+2)+sqrt(1/(x^2-x-3/4)) ?

The domain of sqrt(x+2)+sqrt(1/(x^2-x-3/4)) is -2 3/2

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domain of sqrt(x+2)+sqrt(1/(x^2-x-3/4))

domain

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

Interval Notation

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

Solution steps

Find non-negative values for radicals:

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

Find undefined (singularity) points:

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

Combine real regions and undefined points for final function domain

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

What is the domain of sqrt(x+2)+sqrt(1/(x^2-x-3/4)) ?
The domain of sqrt(x+2)+sqrt(1/(x^2-x-3/4)) is -2<= x<-1/2 \lor x> 3/2