jika f(x) = x-1 dan (g.f) (x) = x^2-x+3, maka rumus fungsi g(2x+3) adalah....

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

pertama-tama, cari g(x) nya.

(g o f)(x) = g(f(x))
x^2 - x + 3 = g (x - 1)
>>> misalkan x - 1 = a, x = a + 1
(a + 1)^2 - (a + 1) + 3 = g(a)
(a + 1)(a + 1) - a - 1 + 3 = g(a)
a^2 + a + a + 1 - a + 2 = g(a)
a^2 + a + 3 = g(a)
x^2 + x + 3 = g(x)

mari kita periksa
(g o f)(x) = g(f(x))
(g o f)(x) = (x - 1)^2 + (x - 1) + 3
(g o f)(x) = (x - 1)(x - 1) + x - 1 + 3
(g o f)(x) = x^2 - x - x + 1 + x + 2
(g o f)(x) = x^2 - x + 3 >> COCOK, dengan demikian g(x) = x^2 + x + 3 BENAR

kemudian cari g(2x + 3)
g(x) = x^2 + x + 3
g(2x + 3) = (2x + 3)^2 + (2x + 3) + 3
g(2x + 3) = (2x + 3)(2x + 3) + 2x + 3 + 3
g(2x + 3) = 4x^2 + 6x + 6x + 9 + 2x + 6
g(2x + 3) = 4x^2 + 14x + 15

semoga membantu