Question

fie funcția f definită pe R cu valori în R unde f (x)=x^2-x^4. Calculați (f•f•f•f)(1)

Answer 1

Răspuns:

Explicație pas cu pas:

f (x) = x^2-x^4

f(f(x)) = (x^2-x^4)^2 - (x^2-x^4)^4

f(f(f(x))) = ((x^2-x^4)^2-(x^2-x^4)^4)^2 - ((x^2-x^4)^2-(x^2-x^4)^4)^4

f(f(f(f(x)))) = (((x^2-x^4)^2-(x^2-x^4)^4)^2-((x^2-x^4)^2-(x^2-x^4)^4)^4)^2 - (((x^2-x^4)^2-(x^2-x^4)^4)^2-((x^2-x^4)^2-(x^2-x^4)^4)^4)^4

f(f(f(f(1)))) = (((1^2-1^4)^2-(1^2-1^4)^4)^2-((1^2-1^4)^2-(1^2-1^4)^4)^4)^2 - (((1^2-1^4)^2-(1^2-1^4)^4)^2-((1^2-1^4)^2-(1^2-1^4)^4)^4)^4

f(f(f(f(1)))) = ((0-0)^2-(0-0)^4)^2 - ((0-0)^2-(0-0)^4)^4

f(f(f(f(1)))) = (0-0)^2 - (0-0)^4

f(f(f(f(1)))) = 0-0

f(f(f(f(1)))) = 0