Diketahui f(x) = 4x - 1 dan (fog)(x) = -2x+3. Rumus fungsi (gofog) (x) =........

jawab
f(x) = 4x - 1
f ⁻¹(x) = 1/4(x+1)

fog(x) = -2x + 3
g(x)= f⁻¹ o (fog)
g(x)= 1/4 ( -2x + 3 + 1)
g(x)= 1/4 (-2x + 4)

gofog(x) = g { fog(x)} = 1/4 { -2 (-2x+3) + 4}
gofog(x) =  1/4 ( 4x - 6 + 4)
gofog(x) = 1/4(4x -2)
gofog(x) = x - 1/2

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

4 (g(x)) = -2 x

karena pangkat tertinggi adalah 1 maka kita misalkan g(x) = ax + b

4 ( ax + b ) - 1 = -2x + 3

4 (ax) + 4b - 1 = -2x + 3

4ax = -2x

4a = -2

a = -1/2

4b - 1 = 3
4b = 4
b = 1

maka g(x) = -1/2 x + 1

(gofog)(x) = g((fog)(x)) = -1/2 ( 4x - 1) + 1
= -2x + 1/2 + 1
= -2x + 1 1/2