Question

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) =x²+x+2
f°g= 2x²+2x+5
f(x) =???

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

Answer 1

Verified answer

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

Answer 2

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