- #1
Andrax
- 117
- 0
This is from a functional equation , i think there is no points in posting it here this is what i ant to prove the functions is from N to N .
let x be a natural number
i want to prove that f(x)=[tex]x^2[/tex]
By induction
suppose that f(x)=[tex]x^2[/tex]
f(0)=0 holds (from the functional equation)
i want to prove that f(x)= [tex](x+1)^2[/tex]
when putting (x,1)(we have f(x+y)+f(x-y) in the equation) I need to know the value of f(x-1) ,does the assumption that f(x)=[tex]x^2[/tex], imply that f(x-1)=[tex](x-1)^2[/tex]
(this is not a homework i just saw this excercise online and decided to do it).
let x be a natural number
i want to prove that f(x)=[tex]x^2[/tex]
By induction
suppose that f(x)=[tex]x^2[/tex]
f(0)=0 holds (from the functional equation)
i want to prove that f(x)= [tex](x+1)^2[/tex]
when putting (x,1)(we have f(x+y)+f(x-y) in the equation) I need to know the value of f(x-1) ,does the assumption that f(x)=[tex]x^2[/tex], imply that f(x-1)=[tex](x-1)^2[/tex]
(this is not a homework i just saw this excercise online and decided to do it).