Răspuns:
[tex](f○f○...○f)(x) = {2}^{n} (x + 1) - 1[/tex]
Explicație pas cu pas:
[tex]f(x) = 2x + 1[/tex]
[tex](f○f)(x) = f(f(x)) = 2×f(x) + 1 = 2×(2x + 1) + 1 = 2²x + 3 = 2²x + 2² - 1 = 2²(x +1) - 1[/tex]
[tex](f○f○f)(x) = f((f○f)(x)) = 2×f((f○f)(x)) + 1= 2×(2²x + 3) + 1 = 2³x + 7 = 2³x + 2³ - 1 = 2³(x+1) - 1[/tex]
[tex](f○f○f○f)(x) = f((f○f○f)(x)) = 2×(2³x + 7) + 1 = 2⁴x + 15 = 2⁴x + 2⁴ - 1 = 2⁴(x+1) - 1[/tex]
[tex]...[/tex]
[tex](f○f○...○f)(x) = {2}^{n} (x + 1) - 1[/tex]
