# What is the domain and range of G(x) = (x^2 +x - 6) ^ (1/2)?

The domain is all the real numbers for which the quantity under the square root is greater and equal to zero.

Hence ${x}^{2} + x - 6 \ge 0$ which holds for $\left(- \infty , - 3\right] U \left[2 , + \infty\right)$ where U symbolizes the union of the two intervals.

Hence $D \left(G\right) = \left(- \infty , - 3\right] U \left[2 , + \infty\right)$

For the range we notice that

$G \left(x\right) = {\left({x}^{2} + x - 6\right)}^{\frac{1}{2}} \ge 0$ hence

$R \left(G\right) = \left[0 , + \infty\right)$