diketahui fungsi f(x)=2x-3 dan (fog) (a) =3 jika g(x) =4x^2-5x+3 maka tentukan nilai a

Pertama tama kamu cari dahulu komposisinya,
(f o g)(x) = f(g(x)) = f(4x^2 - 5x + 3)
(f o g)(x) = 2(4x^2 - 5x + 3) - 3
(f o g)(x) = 8x^2 - 10x + 6 - 3 = 8x^2 - 10x + 3
(f o g)(a) = 3
8a^2 - 10a + 3 = 3
8a^2 - 10a = 0
a(8a - 10) = 0
a = 0 atau a = 10/8 = 5/4

fog(a) = 3 artinya:

[tex]2g(a) - 3 = 3 \\ 2g(a) = 6 \\ g(a) = 3[/tex]

g(a) = 3 artinya:

[tex]4 {a}^{2} - 5a + 3 = 3 \\ 4 {a}^{2} - 5a = 0 \\ 4 {a}^{2} = 5a \\ 4a = 5 \\ a = \frac{5}{4} [/tex]
Jadi a=5/4=1.25