Given :
$$f(k+1) = 2.(k-1) + f(a)+f(b)$$ $$a+b=k+1 $$ a,b are positive integers
We have to prove that $$f(x)\leq{x}^{2}$$ using induction for 1<=x<=k
So we will prove $$f(k+1)\leq{(k+1)}^{2}$$ When x=k+1, $$f(k+1) = 2.(k-1) + f(a)+f(b)$$ $$f(k+1)\leq 2.(k-1) + {a}^{2}+{b}^{2}$$
How to proceed further?