diketahui f : R-R dan g : R-R . jika f(x) = 3x - 2 dan g(x) = x per x-1 . invers f bundaran g (x) adalah

f(x) = 3x - 2
g(x) = x / (x - 1)
(f o g) -¹(x) ?

(f o g) (x) = f (g(x))

(f o g) (x) = 3(x / (x - 1) ) - 2

(f o g) (x) (3x / (x - 1) ) - 2

kali silang

(f o g) (x) = (3x - 2(x - 1) ) / (x - 1)

(f o g) (x) = ( 3x - 2x + 2 ) / (x - 1)

(f o g) (x) = (x + 2) / (x - 1)

(f o g) (x) = y

y = (x + 2) / (x - 1)

y(x - 1) = (x + 2)

xy - y = x + 2

xy - x = y + 2

x (y - 1) = y + 2

x = (y + 2) / (y - 1)

(f o g) -¹(x) = (x + 2) / (x - 1)


maka f bundaran g invers adalah
(f o g) -¹(x) = (x + 2) / (x - 1)

gof^-1 (x) = g(f(x))
= 1 (x-1/x) + 3
= 3x + 2 / 3x + 3
y = x
y = 3x + 2 / 3x + 3
y (3x + 3) = 3x + 2
3xy + 3y = 3x + 2
3xy - 3x = -3y + 2
x (3y - 3) = -3y + 2
y = -3y + 2 / 3y - 3
Jadi fungsi (gof)^-1 (x) = -3x + 2 / 3x -3