Question

Sendo f(x)= $\frac{1-x}{1+x'}$, x≠-1 determine:
a) f(f(f(2)))
bf(f(x))

Answer 1

f(f(f(2)))

f(2) = $\frac{1-2}{1+2} = - \frac{1}{3}$

f(f(-1/3))

f(- 1/3) = $\frac{1- (- \frac{1}{3}) }{1+ (- \frac{1}{3})} = \frac{1+ \frac{1}{3} }{1- \frac{1}{3}} = \frac{ \frac{4}{3} }{ \frac{2}{3} } = \frac{4}{3} . \frac{3}{2} = \frac{4}{2} = 2$

f(2) = -1/3

b) f(f(x)) = 2