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Find the domain of the composite function, hog

H(x)=√x , g(x)=-x+3

1 answer

hog = h(g(x)) = h(-x+3) = √(-x+3)

The term in the square root cannot take negative values. It must be greater than (or equal to) zero.

-x + 3 >= 0
-x >= -3
x =< 3

Hence, the domain of x is given by (-∞, 3]
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