Komposisi FUNGSI 100 Point 1) g°f(x) = 2x²+4x+5 g(x) =2x +3 f(x) =?????? 2) f°g=12x²+32x+26 g(x) =2x+3 f(x) =???? 3) F°g= x²+6x+7 f(x) =x+3 g(x) =???? 4) g(x) =

1) g(x) = 2x + 3
(g o f)(x) = 2x² + 4x + 5
g(f(x)) = 2x² + 4x + 5
2 f(x) + 3 = 2x² + 4x + 5
2 f(x) = 2x² + 4x + 2
f(x) = x² + 2x + 1

2) g(x) = 2x + 3
(f o g)(x) = 12x² + 32x + 26
f(g(x)) = 12x² + 32x + 26
f(2x + 3) = 12x² + 32x + 26
Misal (2x + 3) = a => 2x = a - 3 => x = (a - 3)/2
f(a) = 12((a - 3)/2)² + 32(a - 3)/2 + 26
f(a) = 12(a² - 6a + 9)/4 + 16(a - 3) + 26
f(a) = 3a² - 18a + 27 + 16a - 48 + 26
f(a) = 3a² - 2a + 5
f(x) = 3x² - 2x + 5

3) f(x) = x + 3
(f o g)(x) = x² + 6x + 7
f(g(x)) = x² + 6x + 7
g(x) + 3 = x² + 6x + 7
g(x) = x² + 6x + 4

4) g(x) = x² + x + 2
(f o g)(x) = 2x² + 2x + 5
f(g(x)) = 2x² + 2x + 4 + 1
f(g(x)) = 2(x² + x + 2) + 1
f(g(x)) = 2g(x) + 1
f(x) = 2x + 1

5) f(x) = x + 2
(g o f)(x) = 2x² + 4x + 1
g(f(x)) = 2x² + 4x + 1
g(x + 2) = 2x² + 4x + 1
Misal (x + 2) = a => x = a - 2
g(a) = 2(a - 2)² + 4(a - 2) + 1
g(a) = 2(a² - 4a + 4) + 4a - 8 + 1
g(a) = 2a² - 8a + 8 + 4a - 7
g(a) = 2a² - 4a + 1
g(x) = 2x² - 4x + 1

1)   g°f(x) = 2x²+4x+5
         g(x) =2x +3
      g(f(x)) = 2. f(x) + 3
      2 . f(x) + 3 = 2x² + 4x + 5
      2 . f(x) = 2x² + 4x + 5 - 3
      2 . f(x) = 2x² + 4x + 2
            f(x) = (2x² + 4x + 2)/2
           f(x) = x² + 2x + 1