Question

Let f(x)=(x-1)/(x+1) then f(f(x)) is​

Answer 1

Answer:

f(f(x)) = -1/x

Step-by-step explanation:

f(f(x))

= f ( (x - 1) / (x + 1) )

= $\frac{\frac{x-1}{x+1} - 1}{\frac{x-1}{x+1} + 1}$

= ( (x - 1) / (x + 1) ) - 1 by ( (x - 1) / (x + 1) ) + 1

= ( (x - 1 - x - 1) / (x + 1) ) by ( (x - 1 + x + 1) / (x + 1) )

= ( -2 / (x + 1) ) / ( 2x / (x + 1) )

= ( -2 / (x + 1) ) x ( (x + 1) / 2x )

[ x + 1 is cancelled ]

= -2 / 2x

[ cancel 2 for both numerator and denominator  ]

= -1 / x

Hope it was easy to understand and hope it helps!