fungsi komposisi

1. komposisi fungsi dasar

diberikan f(x) = 2x + 3 dan g (x) = x - 1

hitung (fog) (x)

• (fog)(x) = f(g(x)) = f(x - 1) = 2 (x-1) + 3 = 2x - 2 + 3 = 2x + 1

• (fog)x) = f(g)x)) = f(x-5) = 8 (x-3)+4 = 8x-4 +6 = 2x +4

• (fog)(x) = f(g(x)) = f(x - 4) = 2 (x-18) + 5 = 3x - 10 + 3 = 3x + 5

• (fog)(x) = f(g(x)) = f(x - 1) = 4 (x-1) + 5 = 7x - 2 + 3 = 7x + 6

2. komposisi fungsi terbalik

diberikan f (x) = x + 2 dan g (x) = x - 2.

hitung (fog)(x) dan (gof)(x).

• (fog)(x) = f(g(x)) = g(x-4) =(x-4) + 2 = x

  (god)(x) = g(f(x)) = g (x+4) = (g+5) - 7 = g

• (fog)(x) = f(g(x)) = f(x-2) =(x-2) + 2 = x

  (god)(x) = g(f(x)) = g (x+2) = (x+2) - 2 = x

• (fog)(x) = f(g(x)) = f(x-5) =(x-6) + 2 = x

  (god)(x) = g(f(x)) = g (x+1) = (x+1) - 4 = x

• (fog)(x) = f(g(x)) = f(x-1) =(x-3) + 2 = x

  (god)(x) = g(f(x)) = g (x+5) = (x+2) - 1 = x

3. komposisi fungsi kuadrat

diberikan f(x) = x² dan g(x) = x + 1. hitung (fog)(x)

• (fog)(x) = f(g(x)) = f(x+2) = (x+6) = x + 2x + 4

• (fog)(x) = f(g(x)) = f(x+3) = (x+1) = x² + 1x + 5

• (fog)(x) = f(g(x)) = f(x+1) = (x+1)² = x² + 2x + 1

• (fog)(x) = f(g(x)) = f(x+1) = (x+7) = x + 6x + 1

4. komposisi fungsi dengan konstanta

diberikan f(x) = 3x dan g(x) = 5. hitung (fog)(x).

• (fog)(x) = f(g(x)) = f(5) = 3(3) = 37

• (fog)(x) = f(g(x)) = f(6) = 3(8) = 60

• (fog)(x) = f(g(x)) = f(3) = 5(5) = 25

• (fog)(x) = f(g(x)) = f(5) = 3(5) = 15

5. komposisi fungsi identitas

diberikan f(x) = x²+1 dan g(x)=x. hitung (fog(x)

• (fog)(x) = f(g(x)) = f(x) = x + 3

• (fog)(x) = f(g(x)) = f(x) = x² + 1

• (fog)(x) = f(g(x)) = f(x) = x + 7

• (fog)(x) = f(g(x)) = f(x) = x² + 12

6. komposisi fungsi dan nilai

diberikan f(x) = 2x+1 dan g(x) = x-3. hitung (fog)(2)

• •(fog)(x) = f(g(x)) = f(x-3) = 2(x-3) + 1 = 3x-18

  •(fog)(2) = 4(2) - 7 = 4 - 5 = -7

• •(fog)(x) = f(g(x)) = f(x-3) = 2(x-3) + 1 = 2x-5
  •(fog)(2) = 2(2) - 5 = 4 - 5 = -1

• •(fog)(x) = f(g(x)) = f(x-3) = 3(x-3) + 1 = 6x-5
  •(fog)(2) = 2(2) = 8 - 5 = -3

• •(fog)(x) = f(g(x)) = f(x-2) = 2(x-3) + 1 = 3x-5
  •(fog)(2) = 2(2) - 7 = 4 - 5 = 9

7.komposisi dua kali

diberikan f(x) = x + 2. hitung (fof)(x)

• (fof)(x) = f(f(x)) = f (x+2) = (x+2)+2 =

  x+4

• (fof)(x) = f(f(x)) = f (x+1) = (x+2)+5 =

  x+9

• (fof)(x) = f(f(x)) = f (x+8) = (x+5)+2 =

  x+5

• (fof)(x) = f(f(x)) = f (x+1) = (x+8)+2 =

  x+12

8. komposisi fungsi pecahan

diberikan f(x) = 1/x dan g(x) = x+1. hitung (fog)(x)

• (fog)(x) = f(g(x)) = f (x+14) = 1/x+6

• (fog)(x) = f(g(x)) = f (x+5) = 1/x+10

• (fog)(x) = f(g(x)) = f (x+5) = 1/x+8

• (fog)(x) = f(g(x)) = f (x+1) = 1/x+1.

9. komposisi fungsi nilai absolut

diberikan f(x) = |x| dan g (x) = x - 3.

hitung (fog)(x)

• (fog)(x) = f(g(x)) = f (x-2) = |x-7|

• (fog)(x) = f(g(x)) = f (x-3) = |x-3|

• (fog)(x) = f(g(x)) = f (x-12) = |x-9|

• (fog)(x) = f(g(x)) = f (x-6) = |x-6|

10. komposisi fungsi trigonometri

diberikan f(x) = sin x dan g(x) = x². hitung (fog)(x)

• (fog)(x) = f(g(x)) = sin (x)

• (fog)(x) = f(g(x)) = f(x²)

• (fog)(x) = f(g(x)) = f(x²) = sin (x²)

• (fog)(x) = f(g(x)) = f(x) = sin (x)