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