Soal No 1-5 Materi Komposisi Fungsi & Fungsi Invers, Tolong Jawaban Beserta Caranya Terimakasih !

²Komposisi dan invers

1. f(x)= x²+2x-8
x = {-,2,-1, 0, 1, 2, 3, 4, 5}
f(-2) =(-2)² +2(-2) - 8
f(-2) = 4 - 4 - 8
f(-2) = -8

f(-1) = 1 -2 -8 = -9
f(0) = 0 + 0 -8 = -8
f(1) = 1 +2 - 8 =-5
f(2) = 4 +4 - 8 = 0
f(3) = 9+6-8 = 7
f(4) = 16 +8 -8 = 16
f(5) = 25+10 -8 = 27
daerah hasil R = (-9, -8, -5, 0, 7, 16, 27)

2. f(x) = 3x² - 2
f(x-1)  = 3(x -1) - 2
f(x-1)= 2x - 3 - 2
f(x-1) = 2x - 5

3. d(x)= 2x² -5x +10
g(x)= 4x - 1
fog(x) = f{g(x)} = f(4x-1)
fog(x) =2(4x-1)² -5(4x-1) +10
fog(x) = 2(16x²-8x+1) - 20x +5 +10
fog(x)= 32 x² -16x +2 - 20x +15
fog(x) = 32x² -36 x + 17

(fog)(-1) = 32(1)- 36(-1) + 17
fog(-1) = 85

fog(x)= 13
32x² - 36x + 17 = 13
32x² -36x + 4 = 0
8x² - 9x + 1 =0
(8x -1)(x -1)= 0
x = 1/8    atau x  = 1
.


4. f(x)=  1 + (2x)/(x-1)
f(x)= (x-1 +2x)/.(x-1)
f(x) = (3x -1)/(x-1)
f⁻¹(x)= (-x +1) /( -x + 3)
f⁻¹(x) = (x-1)/(x-3)

5. f(x)= 2x+1
g(x)= 3 - x
(gof)(x) = g(f(x)) = g(2x+1)
gof(x)= 3 - (2x+1) = 3  - 2x -1
gof(x)= 2 - 2x
y = 2 - 2x
2x =2 -y
x = 1 - 1/2 y

(gof)⁻¹(x)= 1 - 1/2 x