Find the function

Let a real function f(x) satisfy following conditions :
1)f(x+y+1)=(\sqrt{f(x)}+\sqrt{f(y)})^2
2)f(0)=1
3)f(x)\geq 0 \ \forall x\in R

Find f(x)

2 Answers

By building the function,

This function turns out to be the same as

f(x)= (x+1)² for all integral values of x

The given information is not sufficient to find the nature of the curve at other real values of x

[339]

Taking x,y=0 f(1)=4

The remaining function can be built by Mathematical Induction

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