SOLUTION: given f(x) = x-3 and g(x) = x^2 +2 a)find(f+g)(x) whats the domain and range b) find f/g (x) whats the domain and range find g/f (x) whats the domain and range thanks fo

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Question 693748: given f(x) = x-3 and g(x) = x^2 +2
a)find(f+g)(x) whats the domain and range
b) find f/g (x) whats the domain and range
find g/f (x) whats the domain and range
thanks for ur help, i am really confused rite now lol
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
given f(x) = x-3 and g(x) = x^2 +2
a)find(f+g)(x) whats the domain and range
(f+g)(x) = f(x)+g(x) = x^2+x-1
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Domain:: All Real Numbers
Range:::
Find the vertex:
x = -b/(2a) = -1/2
f(-1/2) = (1/4)-(1/2)-1 = -5/4
Range is "All Real Numbers >= -5/4"
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b) find f/g (x) whats the domain and range
f/g = f(x)/g(x) = (x-3)/(x^2+2)
Domain: All Real Numbers as there are no vertical asymptotes.
Range: All Real numbers except y = 0 because that is a horizontal asymptote.
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find g/f (x) whats the domain and range
g/f = g(x)/f(x) = (x^2+2)/(x-3)
Domain: All Real Numbers except x = 3, which is a vertical asymptote.
Range: All Real Numbers because there is no horizontal asymptote.
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Cheers,
Stan H.