# Doubts from function

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A putnam problem

What if f(x)=x

F(x) = x doesn't satisfy the condition f(x) >_ 0 for all x belongs to R

Sorry for wrong thought

This problem solved in stackexchange seen 2 or 3 month before

I don't think that this give contradiction

Bro this function is not infinitely differentiable, infact any polynomial with finite degree will be finitely differentiable

No bro that function is infinitely diffentiable

That promises continuity of function , not infinte differentiability

Any polynomial is infinitely differentiable

Since f:R-R is under consideration ,so we can take 'I' to be the real number line . Hence we can assume f to be a function infinitely differentiable over all x€R

f(x)=sin²(πx/2)

Just an example,we can solve graphically too ig

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