Question

4) jika (g-¹of-¹) (x) = 2x-5/3x-1, x tidak sama dengan 1/3 dan f(x) = x-2 , maka g(x) =
A. 5x+1/2-3x
b. 5x-1/3x+2
c. 7x-9/3x-2
d. 7x+9/2-3x
e. 5x-1/3x-2

5) jika (fog-¹)(x) = 2/3x-1 , x tidak sama dengan 1/3 dan f-¹(x) = x-2 , maka g(x) =?
A. 7x+2/3x
b. 2-5x/3x
c. x+4/3x+6
d. x/3x-6
e. x+4/3x+2

Answer 1

Verified answer

Jawab

(4)
f(x)= x  -  2
(g⁻¹ o f⁻¹)(x) = (2x -5)/(3x -1)
g⁻¹(x) =  {g⁻¹ o f⁻¹}o f(x) = (g⁻¹o f⁻¹){ f(x)} =
g⁻¹(x)= (2. f(x) - 5) / (3. f(x)  -1)
g⁻¹ (x)= {2(x-2) - 5}/{3(x-2) - 1}
g⁻¹(x)= (2x -4 - 5)/(3x -6 -1)
g⁻¹(x) = (2x -9)/(3x - 7)
g(x)= {g⁻¹(x)}⁻¹ = (7x +9)/(-3x +2)
g(x)= (7x +9)/(2 - 3x)

(5)
fog⁻¹(x)  = 2/(3x -1)
f⁻¹(x) = x - 1
g⁻¹(x)= f⁻¹ o (fog⁻¹)
g⁻¹ (x)=  f⁻¹ {fog⁻¹}(x)
g⁻¹(x)= f⁻¹ {2/(3x -1)}
g⁻¹(x)= 2/(3x -1) - 2
g⁻¹(x)= {2 - 2(3x-1)}/(3x-1)
g⁻¹(x)= (2 -6x +2) / (3x - 1)
g⁻¹(x)= (-6x + 4)/(3x -1)
g (x) = (x +4)/(3x +6)