If f x - y 2 - f x - f y 2 for all x - y - R and f - o - - 1 - f o - 1 then f2-

The correct option is A 1 2 let f(x)=ax+b f(0)=1 b=1 f'(0)= 1 a= 1 f(x)=1 x f(2)= 1 ...

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Constant Function

If f x + y...

Question

If $f (\frac{x + y}{2}) = \frac{f (x) + f (y)}{2}$ for all $x, y \in R$ and $f^{'} (o) = - 1, f (o) = 1$ then $f (2) =$

\frac{1}{2}

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\frac{- 1}{2}

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Solution

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Similar questions

f (\frac{x + y}{2}) = \frac{f (x) + f (y)}{2} \forall x, y \in R

f^{'} : (0) = - 1, f (0) = 1,

f (2) = ?

f : R \to R

f (x + y) f (x - y) = (f (x) + f (y))^{2} - 4 x^{2} f (y) . . . . . . . . . . (1)

x, y \in R

R

x, y ϵ R

f (n) = n, n ϵ N

If $f (x) = c o s (l o g x)$ , then $f (x^{2}), f (y)^{2} - \frac{1}{2} {f (\frac{x^{2}}{y^{2}}) + f (x^{2} y^{2})}$ has the value

f (x + 2) = \frac{1}{2} {f (x + 1) + \frac{4}{f (x)}}

f (x) > 0

x \in R

lim x \to \infty f (x)

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