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

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Answer 1 · 2015-10-05T23:55:33

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

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

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