Consider the function ƒ : [0, ∞) → [0, ∞) defined by X f(x) = 1². 1+x Prove that the following equation holds for all n E N and all x = [0, ∞): ƒn (x) = X 1+nx (Note: fn is the function obtained by composing f with itself n times. For example, f² = ƒoƒ and f5 = ƒoƒoƒoƒoƒ, etc.) O

Determine using induction all the positive integer values of n for n^3 > 2^n. Prove your answer using mathematical induction.    Please read the question. This is NOT asking to prove that all integers satisfy this, it is asking to find the integers that do satisfy it via induction.  Please explain every step.

Prove by induction: For all integers N ≥ 1, 2 + 6 + 10 +...+ (4N-2) = 2N^2

pls help, thx