Question

If x ≠ 1 and \[f\left( x \right) = \frac{x + 1}{x - 1}\] is a real function, then f(f(f(2))) is

 

Options

• (a) 1

• (b) 2
  

• (c) 3

• (d) 4

   

Answer 1

(c) 3 \[f\left( x \right) = \frac{x + 1}{x - 1}\] \[f(f(f(2))) \]
\[ = f\left( f\left( \frac{2 + 1}{2 - 1} \right) \right)\]
\[ = f\left( f(3) \right)\]
\[ = f\left( \frac{3 + 1}{3 - 1} \right)\]
\[ = f(2) = 3\]