Question

Função composta.
sendo f(x)$\frac{3x+1}{x-1} , determinef(f(x)).$

Answer 1

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

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

$g(x) = \frac{(\frac{9x+3+x-1}{x-1})}{(\frac{3x+1-x+1}{x-1})} = \frac{9x+3+x-1}{3x+1-x+1} = \frac{10x +2}{2x+2} =\frac{5x+1}{x+1}$