Jika f(x) = x² + 1 dan g(x) = 2x – 1 maka tentukan (g o f)^-1(x)

Jawab

gof(x)=  g{ f(x)} = g (x²+1)
= 2(x² +1)  -1
= 2x² + 1

2x²  = y -1
x²  = 1/2 y – 1/2
x = √(1/2 y – 1/2)

(gof) ⁻¹ (x) = √(1/2 x – 1/2)
atau  (gof)⁻¹= 1/2 √(2x – 2)

F(x) = x² + 1
g(x) = 2x – 1

(gof)(x) = y
= 2(x² + 1) – 1
= 2x² + 1

y = 2x² + 1
x = √((y – 1)/2)

(gof)^-1 (x)
= √((x – 1)/2) ✔