1. diketahui (gof) (x)=x+2/x dan f(x) x+1/x-1 tentukan nilai g(2) 2.diketahui (gof) (x)=x-2/x+4 dan f(x)=x+2 tentukan nilai g(4)

Langsung aja y

1.
misal :
x+1 / x-1 = a
x+1 = xa - a
xa - x = 1 + a
x(a-1) = 1+a
x = (1+a) / (a-1)

soal menjadi →
(gof)(x) = g{f(x)}

(x+2) / x = g(x+1 / x-1)
(x+2) / x = g(a)
{(1+a) / (a-1) + 2} : (1+a) / (a-1) = g(a)
{(1+a+2a-2) / (a-1)} × (a-1) / (1+a) = g(a)
(3a-1) / (a-1) × (a-1) / (1+a) = g(a)
(3a²-3a-a+1) / (a+a²-1-a) = g(a)
(3a²-4a+1) / (a²-1) = g(a)

g(2) = (3(2)² - 4(2) + 1) / (2² - 1)
g(2) = (12 - 8 + 1) / 3
g(2) = 5/3

2.
(gof)(x) = g{f(x)}
(x-2) / (x+4) = g(x+2)

misal :
x+2 = a
x = a-2

soal menjadi →
g(a) = (a-2-2) / (a-2+4)
g(a) = (a-4) / (a+2)

g(4) = (4-4) / (4+2)
g(4) = 0 / 6
g(4) = 0

Semoga berguna +_+