fungsi komposisi matematika f(x)=2-x g(x)=x2-1 h(x)=-2x+2 d tanya a.(fog) (2)= b.(goh) (3)= c.(foh) (1)= d.(hog) (x)= e.(hog) (x)= f.((fog)oh) (x)= g.(fo(goh

f(x) = 2 - x
g(x) = [tex]x^2[/tex] - 1
h(x) = -2x + 2
a. (fog)(x) = 2 - ([tex]x^2[/tex] - 1) = 2 - [tex]x^2[/tex] +1 = 3 - [tex]x^2[/tex]
(fog)(2) = 3 - [tex]2^2[/tex] = 3 - 4 = -1

b. (goh)(x) = [tex](-2x+2)^2[/tex] - 1 = [tex]4x^2[/tex] - 8x + 4 - 1 = [tex]4x^2[/tex] - 8x + 3
(goh)(3) = [tex]4(3^2)[/tex] - 8(3) + 3 = 36 - 24 + 3 = 15

c. (foh)(x) = 2 - (-2x + 2) = 2 + 2x - 2 = 2x
(foh)(1) = 2 (1) = 2

f. (fog)(x) = 3 - [tex]x^2[/tex] (lihat soal a)
((fog)oh) (x) = 3 - [tex](-2x+2)^2[/tex] = 3 - ([tex]4x^2[/tex] - 8x + 4) = 3 - [tex]4x^2[/tex] + 8x - 4 = [tex]-4x^2[/tex] + 8x - 1

g. (goh)(x) = [tex]4x^2[/tex] - 8x + 3 (lihat soal b)
(fo(goh))(x) = 2 - ([tex]4x^2[/tex] - 8x + 3) = 2 - [tex]4x^2[/tex] + 8x - 3 = [tex]-4x^2[/tex] + 8x - 1

h. (goh)(x) = [tex]4x^2[/tex] - 8x + 3 (lihat soal b)
((goh)of)(x) = [tex]4(2-x)^2[/tex] - 8(2 - x) + 3 = 4(4 - 4x + [tex]x^2[/tex]) - 16 + 8x + 3 = 16 - 16x + 4[tex]x^2[/tex] - 16 + 8x + 3 = 4[tex]x^2[/tex] - 8x + 3

i. (foh)(x) = 2x (lihat soal c)
(go(foh))(x) = [tex](2x)^2[/tex] - 1 = 4[tex]x^2[/tex] - 1

j. (fog)(x) = 3 - [tex]x^2[/tex] (lihat soal a)
(ho(fog))(x) = -2(3 - [tex]x^2[/tex]) + 2 = -6 + 2[tex]x^2[/tex] + 2 = 2[tex]x^2[/tex] - 4