Question

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

Answer 1

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>=0` which holds for `(-oo,-3]U[2,+oo)` where U symbolizes the union of the two intervals.

Hence `D(G)=(-oo,-3]U[2,+oo)`

For the range we notice that

`G(x)=(x^2+x-6)^(1/2)>=0` hence

`R(G)=[0,+oo)`