Jika diketahui f (x) = 2x + 1 dan g (x) = x² – 2x + 2 ,maka nilai dari (f-¹ og-¹) (x) adalah…​

Jawaban:

(f-¹ o g-¹)(x) = √x-1 /2

Penjelasan dengan langkah-langkah:

Diketahui :

f(x) = 2x + 1

g(x) = x²-2x+2

Ditanya :

nilai (f-¹ o g-¹)(x) =?

Jawab :

(f-¹ o g-¹)(x) = (g o f)-¹(x)

(g o f)(x) = g(f(x))

= g(2x + 1)

= (2x + 1)² – 2(2x + 1) + 2

= 4x²+ 4x + 1 – 4x – 2 +2

= 4x² + 1

(g o f)(x) = 4x²+1

(g o f)(x) = 4x² + 1

y = 4x² + 1

y-1 = 4x²

y – 1 /4 = x²

√y-1 /√4 = x

x = √y-1 /2

(g o f)-¹(y) = √y-1 /2

(g o f)-¹(x) = √x-1 /2

(f-¹ o g-¹)(x) = √x-1 /2

semoga membantu 🙂

Terima kasih