Question

Tolonginn qwannn makasih

Answer 1

Diketahui:
f(x – 1) = 4x – 4
g(2x) = 1 + ¼ x²
h(√x) = √x – 3
Ditanyakan:
a. f(x), g(x), h(x)
b. f⁻¹(x), g⁻¹(x), h⁻¹(x)
c. (f o g o h)(x)
Jawab:
a. f(x – 1) = 4x – 4 = 4(x – 1)
→ f(x) = 4x
g(2x) = 1 + ¼ x² = 1 + 1/16 (2x)²
→ g(x) = 1 + 1/16 x²
h(√x) = √x – 3
→ h(x) = x – 3
b. f(x) = 4x
↔ x = f(x)/4
→ f⁻¹(x) = x/4
g(x) = 1 + 1/16 x²
↔ g(x) – 1 = 1/16 x²
↔ 16(g(x) – 1) = x²
↔ x = ±√16(g(x) – 1)
       = ±4√(g(x) – 1)
→ g⁻¹(x) = ±4√(x – 1)
h(x) = x – 3
↔ x = h(x) + 3
→ h⁻¹(x) = x + 3
c. (f o g o h)(x)
= (f o g)(h(x))
= (f o g)(x – 3)
= f(g(x – 3))
= f(1 + 1/16 (x – 3)²)
= 4(1 + 1/16 (x – 3)²)
= 4 + ¼ (x – 3)²
= 4 + ¼ x² – 6/4 x + 9/4
= ¼ x² – 3/2 x + 6 1/4