Question

Diketahui fungsi f: R---->R dengan f(x) = x^{2} - 4x + 2 dan fungsi g: R---->R dengan g(x) = 3x - 7
a) (g o f)(x)
b) (f o g)(x)
c) (g o f)(5)
d) (f o g)(10)


f(x) = x + 5
g(x) = 2x - 10
tentukan
( fog ) (x)
( gof ) (x)
( gof ) (4)

Answer 1

(gof)(x) = g(f(x))
(gof)(x) = g(x^2 - 4x + 2)
(gof)(x) = 3(x^2 - 4x + 2) - 7
(gof)(x) = 3x^2 - 12x + 6 - 7
(gof)(x) = 3x^2 - 12x - 1

(fog)(x) = f(g(x))
(fog)(x) = f(3x - 7)
(fog)(x) = (3x - 7)^2 - 4(3x - 7) +2
(fog)(x) = (3x - 7)(3x - 7) - 12x + 28  + 2
(fog)(x) = 9x^2 - 21x - 21x + 49 - 12x + 30
(fog)(x) = 9x^2 - 54x +79

(gof)(x) = 3x^2 - 12x - 1
(gof)(5) = 3.5^2 - 12.5 - 1
(gof)(5) = 3.25 - 60 -1
(gof)(5) = 75 - 60 -1
(gof)(5) = 14

(fog)(x) = 9x^2 - 54x +79
(fog)(10) = 9.10^2 - 54.10 +79
(fog)(10) = 9.100 - 540 +79
(fog)(10) = 900 - 540 + 79 
(fog)(10) = 360 + 79
(fog)(10) = 439

coba dikoreksi lagi, siapa tahu saya ada yg keliru gan