Question

Se considera functia f:R-R f(x)=x^2-3x. Sa se rezolve ecuatia (fof)(x)=4​

Answer 1

Răspuns:

Explicație pas cu pas:

f : R --> R   ;  f(x) = x²- 3x

f o f = 4 <=>  f(f(x)) = (x²-3x)² - 3(x²-3x)  = 4 =>

x⁴-6x³+9x²-3x²+9x-4 = 0 <=>

x⁴-6x³+6x²+9x-4 = 0 <=>

(x+1)(x-4)(x²-3x+1) = 0 =>

x₁ = -1 ; x₂ = 4 ;

x²-3x+1 = 0 => x₃,₄ = [3±√(9-4)]/2 =>

x₃ = (3-√5)/2 ; x₄ = (3+√5)/2