Tentukan (fog)-(gof)(x), jika f(x)=-x2+1, dan g(x)=2x-2!​

Jawab:

Tentukan (fog) – (gof)(x),

Jika f(x)=-x²+ 1, dan g(x)=2x – 2 ?

Penjelasan:

_________

Mencari nilai (fog)(x) dan (gof)(x):

1. (fog)(x)

= f(g(x))

= f(2x – 2)

= -(2x – 2)² + 1

= -4x² + 8x – 4 + 1

(fog)(x) = -4x² + 8x – 3

2. (gof)(x)

= g(f(x))

= g(-x² + 1)

= -2(x² + 2) – 2

= -2x²

Maka,

(fog)-(gof)(x)

= -4x² + 8x – 3 – (-2x²)

= -6x² + 8x – 3

Semoga bermanfaat-,