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  4. If x≠ 1 and f(x)=(x+1/x-1) is a real function, then fff(2) is:

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Q. If $ x\ne 1 $ and $ f(x)=\frac{x+1}{x-1} $ is a real function, then $ fff(2) $ is:

KEAMKEAM 2001

Solution:

$ \because $ $ f(x)=\frac{x+1}{x-1} $ $ \therefore $ $ f(2)=\frac{2+1}{2-1}=3 $ $ f\{f(2)\}=f(3)=\frac{3+1}{3-1}=\frac{4}{2}=2 $ and $ f[f\{f(2)\}]=f(2)=\frac{2+1}{2-1}=3 $