SOLUTION: f(x)= 1/x-1; g(x)= √x find f(g(g)) and g(f(g)). State the domain.

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Question 348400: f(x)= 1/x-1; g(x)= √x
find f(g(g)) and g(f(g)). State the domain.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
f(x)= 1/(x-1); g(x)= √x
-------
find f(g(g)) and g(f(g)).
f[g(sqrt(x))]
= f[x^(1/4)]
---
= 1/[x^(1/4) - 1]
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Domain of f[g(g(x)] is all non-negative Real Numbers.
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find g[f(g)]
g[f(sqrt(x)]
= g[1/(sqrt(x)-1]
---
= sqrt[1/(sqrt(x)-1]
-----------------------
Domain of g[f(g)] = is all non-negative Real Numbers.
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Cheers,
Stan H.