diketahui f (x) = 2 - x dan g (x) = 2x + a + 1. jika (f o g) (x) = (g o f) (x). tentukan nilai a ! pake caranya.

diketahui f (x) = 2 – x dan g (x) = 2x + a + 1. jika (f o g) (x) = (g o f) (x). tentukan nilai a ! pake caranya.

F (g (x)) = f (2x + a + 1)
   = 2 – (2x +a+1)
   = 2 – 2x – a – 1
   = – 2x – a + 1
g (f(x)) = g (2-x)
      = 2 (2-x) + a + 1
      = 4 – 2x + a + 1
   = -2x + a + 5
f (g (x)) = g (f(x))
-2x – a + 1 = -2x + a + 5
– 2 a = 4
Jadi, a = 4 / -2 = – 2

$(fog)(x)=(gof)(x)\ f(g(x))=g(f(x))\ f(2x+a+1)=g(2-x)\ 2-(2x+a+1)=2(2-x)+a+1\ -2x-a+1=-2x+a+5\ -a+1=a+5\ -a-a=5-1\ -2a=4\ a=-2$