Question

Sendo f (x) = 2x+1; então, f (f (x) ) vale X-2

Answer 1

$f(f(x)) = 2 (\frac{f(x) + 1}{(f(x)}) -2\\\\ = \frac{2(\frac{2x+1}{x-2}) + 1 }{(\frac{2x+1}{x-2}) -2}\\\\ = \frac{\frac{4x+2 + x-2}{x-2} }{\frac{2x+1 -2x+4 }{ x-2}}\\\\ = \frac{5x}{x-2} . \frac{x-2}{5} \\\\ = x$

Portanto, f(f(x)) = x