Jawab:

fungsi komposisi

fungsi invers

1) f(x)=  2x² + 1  dan  g(x) = x + 3

a. (fog)(x) =  f{x+ 3} = 2(x +3)² + 1

= 2(x²+6x + 9) + 1

= 2x² +12x + 18 +1

= 2x² +12x +19

b. (gof)(x)=  g{2x²+1)

= 2x²+ 1 +  3

= 2x² + 4

2)  f(x) =  x - 2 dan  (fog)(x) = 3x+ 1

g(x) - 2 =  3x+ 1

g(x)=  3x+ 1 + 2

g(x) = 3x+  3

3)  g(x) = x+ 4  dan  fog(x)=  4x /(x + 5)

f{x + 4}=  4x/ (x + 5)

f(x) =  4(x- 4)/ (x - 4 + 5)

f(x)=   (4x - 16)/ (x + 1)

4. f(x) = x + 2  danm  fog(x) = x² -6x + 9

f{ g(x)} =  x² -6x + 9

g(x) + 2 = x² - 6x + 9

g(x) =  x² -6x +  7

5.  f(x) =  x²  +5x - 3 dan  gof(x) =  2x² + 10x - 3

g {x² +5x - 3} =  2x² +10x - 3

g {x² +5x - 3} =  2(x²+ 5x - 3)  + 3

g(x) =  2x + 3

g(x + 2) = 2(x + 2) +  3

g(x + 2) =  4x + 4 +  3

g(x + 2) =  4x + 7