If \({\rm{g}}\left( {\rm{x}} \right) = \frac{1}{{{\rm{f}}\left( {\rm{x}} \right)}}\) and f(x) = x, x ≠ 0, then which one of the following is correct?

f(g(f(g(g(f(g(x))))))) = g(g(f(g(f(x)))))

f(f(f(g(g(f(x)))))) = g(g(f(g(f(x)))))

f(f(g(g(g(f(x)))))) = g(g(f(g(f(x)))))

f(f(f(g(g(f(x)))))) = f(f(f(g(f(x)))))

If \({\rm{g}}\left( {\rm{x}} \right) = \frac{1}{{{\rm{f}}\left( {\rm{x

1.	If \({\rm{g}}\left( {\rm{x}} \right) = \frac{1}{{{\rm{f}}\left( {\rm{x}} \right)}}\) and f(x) = x, x ≠ 0, then which one of the following is correct?
A.	f(f(f(g(g(f(x)))))) = g(g(f(g(f(x)))))
B.	f(f(g(g(g(f(x)))))) = g(g(f(g(f(x)))))
C.	f(g(f(g(g(f(g(x))))))) = g(g(f(g(f(x)))))
D.	f(f(f(g(g(f(x)))))) = f(f(f(g(f(x)))))
Answer» C. f(g(f(g(g(f(g(x))))))) = g(g(f(g(f(x)))))

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