Question

Diketahui f (x) =1-3x dan g (x) = x2-1 jika (g o f)(a) =3 maka nilai a adalah. .

Answer 1

F(x) = 1 - 3x
g(x) = x^2 - 1

(g•f) (x) = x^2 - 1
= (1-3x)^2 - 1
= 1 - 6x + 9x^2 - 1
= 9x^2 - 6x

(g•f) (a) = 3
9x^2 - 6x = 3
9a^2 - 6a = 3
9a^2 - 6a - 3 = 0
(3a+1) (3a-1) (3a+2) = 0
maka a1 = -1/3
a2 = 1/3
dan a3 = -2/3

Answer 2

F(x) = 1 - 3x
g(x) = x² - 1
(gof)(a) = 3
a = ............?

Penyelesaian :

(gof)(x) = g(f(x)
             = (1 - 3x)² - 1
             = (9x² - 6x + 1) - 1
             = 9x² - 6x

(gof)(a) = 3
3 = 9(a)² - 6(a)
1 = 3(a)² - 2(a)
1 = 3a² - 2a
3a² - 2a - 1 = 0
(3a + 1) (a - 1) = 0

3a + 1 = 0
a = -⅓

a - 1 = 0
a = 1

Jadi, nilai a adalah -⅓ atau 1