jika f(x)=x+1/x dan g(x)=x-1/x.Tentukan f(g(x))

Fungsi Komposisi

f(x) = x + 1/x = (x² + 1)/x
g(x) = x - 1/x = (x² - 1)/x

f(g(x))
= x((x² - 1)²/x + 1) / ((x² -1)² + x)/(x² - 1)
= (x⁴ - 2x² + x + 1) / (x² - 1)

f(g(x)=(x-1/x) + 1/(x-1/x)
        
         = ((x-I/x)^2 / (x-1/x)) + I/(x-1/x)

          =((x-1/x) / (x-1/x)) + 1/1

          =1 + 1

          = 2