Diketahui f(x)=x^2+nx dan g(x)=2x-3. Jika

Nilai dari 5n adalah 4.

Pembahasan

Diketahui fungsi f(x) = x^2 + nx dan g(x) = 2x - 3.
Diketahui juga bahwa (fog)(2) = (gof)(-2).

Langkah 1: Cari (fog)(x)
(fog)(x) = f(g(x))
(fog)(x) = f(2x - 3)
(fog)(x) = (2x - 3)^2 + n(2x - 3)
(fog)(x) = (4x^2 - 12x + 9) + (2nx - 3n)
(fog)(x) = 4x^2 + (2n - 12)x + (9 - 3n)

Langkah 2: Hitung (fog)(2)
(fog)(2) = 4(2)^2 + (2n - 12)(2) + (9 - 3n)
(fog)(2) = 4(4) + (4n - 24) + (9 - 3n)
(fog)(2) = 16 + 4n - 24 + 9 - 3n
(fog)(2) = n - 8 + 9
(fog)(2) = n + 1

Langkah 3: Cari (gof)(x)
(gof)(x) = g(f(x))
(gof)(x) = g(x^2 + nx)
(gof)(x) = 2(x^2 + nx) - 3
(gof)(x) = 2x^2 + 2nx - 3

Langkah 4: Hitung (gof)(-2)
(gof)(-2) = 2(-2)^2 + 2n(-2) - 3
(gof)(-2) = 2(4) - 4n - 3
(gof)(-2) = 8 - 4n - 3
(gof)(-2) = 5 - 4n

Langkah 5: Samakan hasil (fog)(2) dan (gof)(-2)
(fog)(2) = (gof)(-2)
n + 1 = 5 - 4n

Langkah 6: Selesaikan untuk n
n + 4n = 5 - 1
5n = 4

Langkah 7: Tentukan nilai dari 5n
Karena kita sudah mendapatkan 5n = 4, maka nilai dari 5n adalah 4.