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If f(x) = \(\rm \frac{x+1}{x-1}\), x ≠ 1, then f{f(x)} = ? 

  1. -1/x
  2. \(\rm \frac{1}{x^2}\)
  3. x 
  4. 2/x

Answer (Detailed Solution Below)

Option 3 : x 
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Detailed Solution

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Concept: 

Composition of function: Let f, and g be any functions then, f ∘ g(x) = f[g(x)]

Calculation:

Here, f(x) = \(\rm \frac{x+1}{x-1}\)

f{f(x)} = \(\rm \frac{f(x)+1}{f(x)-1}\)

= \(\rm \frac{\frac{x+1}{x-1}+1}{\frac{x+1}{x-1}-1}\)

= \(\rm \frac{2x}{2}\)

= x

Hence, option (3) is correct.

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