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Question

If g(x)=1f(x) 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)))))
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B
f(g(f(g(g(f(g(x)))))))=g(g(f(g(f(x)))))
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C
f(g(f(g(g(f(g(x)))))))=f(g(f(g(f(x)))))
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D
f(f(f(g(g(f(x))))))=f(f(f(g(f(x)))))
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Solution

The correct option is C f(g(f(g(g(f(g(x)))))))=f(g(f(g(f(x)))))
From the given data, it is evident that gof(x)=1x=fog(x)
f(f(f(g(g(f(x))))))=x and g(g(f(g(f(x)))))=1x
f(g(f(g(g(f(g(x)))))))=x and g(g(f(g(f(x)))))=1x
f(g(f(g(g(f(g(x)))))))=x and f(g(f(g(f(x)))))=x
f(f(f(g(g(f(x))))))=x and f(f(f(g(f(x)))))=1x

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