Question

Sabendo que f(x)=x ao quadrado +1 e g(x)=x -1. calcule f(g(x)) - g(f(x))/x-1 ​

Answer 1

f(x)=x²+1

g(x)=x-1

$\frac{f(g(x)) - g(f(x))}{x-1} =\frac{(g(x)^{2}+1)-(f(x)-1)}{x-1} =\frac{((x-1)^{2}+1)-(x^{2}+1-1)}{x-1}=\frac{(x^{2}-2x+1+1)-x^{2}}{x-1}$  <=>

<=>   $\frac{-2x+2}{x-1} =\frac{-2.(x-1)}{x-1} =-2$