Question

Diketahui g(x) = x/x - 1 dan (f o g) (x) = 3x - 1 / x - 1 maka f(-1) =

Answer 1

G(x) = x/(x-1)
fog(x) = (3x-1)/(x-1)
f(g(x)) = (3x-1)/(x-1)
f(x/(x-1)) = (3x-1)/(x-1)

misal
x/(x-1) = p
x = p(x-1)
x = px - p
x-px = -p
x(1-p) = -p
x = -p/(1-p)

sehingga
f(p) = {3(-p/(1-p))-1}/{(-p/(1-p))-1}
f(p) = {(-3p/(1-p))-1)}/{(-p/(1-p)) -1}
f(p) = {(-3p-(1-p))/(1-p)} / {(-p-(1-p))/(1-p)}
f(p) = {(-3p-1+p)/(1-p)} / {(-p-1+p)/(1-p)}
f(p) = {(-2p-1)/(1-p)} / {-1/(1-p)}
f(p) = {(-2p-1)/(1-p)} * -(1-p)
f(p) = -(-2p-1)
f(p) = 2p+1
f(x) = 2x+1

maka f(-1) = 2(-1)+1 = -2+1 = -1