SOLUTION: Find the domain of gf if f (X) =x^2 and g(X) = square root of x-6

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Question 1190718: Find the domain of gf if f (X) =x^2 and g(X) = square root of x-6
Answer by ikleyn(52802) About Me  (Show Source):
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Find the domain of gf if f(X) =x^2 and g(X) = square root of (x-6)
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The composite function  (gof)(x) is  (gof)(x) = sqrt%28x%5E2-6%29.


This composite function is defined if and only if  x^2-6 >= 0,  or  x^2 >= 6.


It means that  the domain is the union of two sets  ( -oo < x <= -sqrt%286%29 )  and  ( sqrt%286%29 <= x < oo ).


In the interval form, it is the same as  (-oo,-sqrt%286%29 ] U [ sqrt%286%29,oo).

Solved and explained.