Question

(Fei-SP) Sendo f(x) = 2x+1/x-2, obter f(f(x))

Answer 1

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