Question

2. Diketahui fungsi f(x) = 2^x+2 x 6^x-4 dan g(x) = 12^x-1 untuk x bilangan asli. Tentukanlah nilai f(x) / g(x) !
3. Diketahui (g o f) (x) = 4x^2 +4x dan g(x) = x^2 -1 . Tentukanlah nilai f(x-2). bisa jawab ini

Answer 1

2. f(x) = 2^x+2  x  6^x-4
g(x) = 12^x-1
f(x)/g(x) = (2^x+2 x 6^x-4) / 12^x-1
= (2^x+2)(6^x-4) / (2^x-1)(6^x-1)
= (2^x-x+2+1) (6^x-x-4+1)
= 2^3 (6^-3)
= 2^3 . 2^-3 . 3^-3
=  3^-3
= 1/3^3
=1/27

3. (g o f) (x) = 4x^2 + 4x
g(x) = x^2 - 1
(g o f) (x) = g(f(x))
4x^2 + 4x = (f(x))^2 - 1
(f(x))^2 = 4x^2 + 4x + 1
(f(x))^2 = (2x + 1)^2
f(x) = 2x + 1

f(x-2) = 2(x-2) + 1 = 2x - 4 + 1 = 2x - 3