SOLUTION: Find the domain and range of the composite function f o g, g o f f(x)=1/x g(x)=x/(x+1)

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Question 785657: Find the domain and range of the composite function
f o g, g o f
f(x)=1/x
g(x)=x/(x+1)

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find the domain and range of the composite function
f(x)=1/x
g(x)=x/(x+1)
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f o g = f[g(x)] = f[x/(x+1)] = (x+1)/x = 1+(1/x)
Domain:: All Real numbers except x = 0
Range: All Real numbers except y = 1
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g o f = g[f(x)] = g[1/x] = (1/x)/((1/x)+1) = (1/x)/(1+x)/x = 1/(1+x)
Domain: All Real Numbers except x = -1
Range:: All Real Numbers except y = 0
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Cheers,
Stan H.
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