Diketahui rumus fungsi f(x) x+2 dan g^-1(x)= x+1 tentukan , a)(gof)^-1 (x) b)jika (fog–¹) (a)=2 hitung nilai a

a) (gof) -1 (x)

g(x) =x+1
gof (x) = (x+2) + 1
= x + 3

gof -1 (x) = x+3
y = x + 3
x = 3-y

fungsi  komposisi dan fungsi invers

f(x)= x+2
g⁻¹(x)= x +1
a) (gof)⁻¹(x)
b) (fog⁻¹)(a) = 2 , a = ...?
.
f(x)= x + 2 ---> f⁻¹(x)= x - 2
g⁻¹(x)=  x +1 --> g(x) = x -1

a) (gof)⁻¹ (x)= (f⁻¹ o g⁻¹)(x) = f⁻¹ {g⁻¹(x)}
(gof)⁻¹ (x) = f⁻¹ (x+1)
(gof)⁻¹ (x) = (x+1) - 2
(gof)⁻¹ (2) = ( x - 1)

b) (fog⁻¹)(a) = 2
f{ g⁻¹(a)} = 2
f( a+1) = 2
(a+1)+2 = 2
a + 1= 0
a = - 1