Jika diketahu f(x)=x²-4 dan g(x)= x/x+1, carilah (f°g) (x) dan (g°f). (x)

jawab

f(x) = x² - 4
g(x) =  x/(x +1)

fog(x) = f { g(x)}
= f { x /(x +1)}
= (x/ (x +1))² - 4
= {x² - 4(x+1)²}/(x+1)²
= ( x² - 4x² - 8x - 4) / (x+1)²
= ( - 3x² - 8x - 4) / (x + 1)²

gof(x) = g { f(x)}
= g{ x² -4 }
= (x²- 4)/ (x² -4+ 1)
= (x² -4)/ (x² - 3)