Jika f(x) = 2x-3 dan (f o g) (x) = 5-2x/x+3 ,maka g-¹(2) =...

langsung aja yy

(fog)(x) = f{g(x)}

5 - 2x / x + 3= 2g(x) - 3

5 - 2x = 2x.g(x) - 3x + 6g(x) - 9

5 - 2x + 3x + 9 = g(x) (2x + 6)

x + 14 = g(x) (2x + 6)

(x + 14) / (2x + 6) = g(x)

maka

gog`¹(x) = x
g{g`¹(x)} = x
g`¹(x) + 14 / 2g`¹(x) + 6 = x
g`¹(x) + 14 = 2x.g`¹(x) + 6x
g`¹(x) - 2x.g`¹(x) = 6x - 14
g`¹(x) (1 - 2x) = 6x - 14
g`¹(x) = 6x - 14 / 1 - 2x

maka
g`¹(2) = 6(2) - 14 / 1 - 2(2)
g`¹(2) = 12 - 14 / 1 - 4
g`¹(2) = -2 / -3
g`¹(2) = ⅔

semoga berguna +_+