Question

$f(x) = {x}^{2} + 1 \: e \: g(x) = x - 1 \: calcule \: \frac{f(g(x)) - g(f(x))} {1 - x}$
resposta =2 ​

Answer 1

Resposta:

$f(x) = {x}^{2} + 1 \\ \\ g(x) = x - 1 \\ \\ f(g(x)) = {(x - 1)}^{2} + 1 \\ \\ f(g(x)) = {x}^{2} - 2x + 1 + 1 \\ \\ \blue{f(g(x)) = {x}^{2} - 2x + 2} \\ \\ g(f(x)) = {x}^{2} + 1 - 1 \\ \\ \orange{g(f(x)) = {x}^{2}} \\ \\ \dfrac{\blue{f(g(x))} \orange{- g(f(x))}}{1 - x} \\ \\ \dfrac{ \red{{x}^{2}} - 2x + 2 \red{ - {x}^{2}} }{1 - x} \\ \\ \dfrac{ 2- 2x }{1 - x} \\ \\ \frac{ 2( \red{1 - x}) }{ \red{1 - x}} \\ \\ 2 \times \red{1} \\ \\ \green{2}$

Bons Estudos!