Question 783533: Find the specified domain
For g(x)=√x+2 and h(x)= 1/x-3, what is the domain of h o g?
This is what I worked out but I am certain it is incorrect.
h(g(x))= 1/(√x+2)-3
x+2=0
x=-2
Domain: (-∞, -2)∪(-2, ∞)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Find the specified domain
For g(x)=√(x+2) and h(x)= 1/(x-3, what is the domain of h o g?
This is what I worked out but I am certain it is incorrect.
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h(g(x))= h[g(x)] = h[sqrt(x+2) = 1/[sqrt(x+2)-3]
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x+2 must be >= 0
x must be >= -2
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But: sqrt(x+2)-3 cannot be zero.
sqrt(x+2) # 3
x+2 # 9
x # 7
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Domain of hog is [-2,7)U(7,+oo)
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Cheers,
Stan H.
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