Fungsi f:R➡R dan g:R➡ ditentukan oleh f(x)=x³ dan g(x)=3×-4.jika a=(g-¹ bundaran f-¹)(8), nilai (f-¹ bundaran g-¹)(10a)=.......

jawab

f(x)= x³
g(x) = 3x - 4

fog(x) = f{g(x)}
= f(3x-4)
= (3x - 4)³
 
(g⁻¹ o f⁻¹)(8) = a
(fog)⁻¹(8) = a
fog(a) = 8
(3a - 4)³ = 8 = 2³
3a - 4 = 2
3a = 6
a = 2


f⁻¹ o g⁻¹ (10a) =y
a= 2 → f⁻¹ o g⁻¹ (20) =  (gof)¹ (20) = y
(gof)(y) = 20
g{f(y)} = 20
g(y³) = 20
3y³- 4 = 20
3y³ = 24
y³ = 24/3  = 8
y³ = 2³
y = 2

f⁻¹ o g⁻¹ (10a) = 2