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Definition of Functions

31.Let f: R >...

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31.Let f: R > R be a differentiable function satisfying f(x/2+y/2)= f(x)/2 +f(y)/2 for all x,y R. If f'(0)=-1 and f(0)=1 then f(x)=

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f

be a differentiable function on

R

f (x + y) = f (x) + f (y) \forall x, y ϵ R

f^{'} (0) = 2

, then the value of

f (4)

f

be a differentiable function from

R

R

| f (x) - f (y) | \leq 2 | x - y |^{3 / 2}

x, y \in R

f (0) = 1

1 \int 0 f^{2} (x) d x

f

be a differential function satisfying

f (x + y) = f (x) + f (y) + (e^{x} - 1) (e^{y} - 1) \forall x, y \in R

f^{'} (0) = 2

. Identify the correct statement(s)?

f

be differentiable function from R to R such that

| f (x) - f (y) | \leq 2 | x - y |^{\frac{3}{2}}

x, y

ε

f (0) = 1

\int_{0}^{1} f^{2} (x) d x

f : R \to R

be a function such that

f (\frac{x + y}{2}) = \frac{f (x) + f (y)}{2}

for all x, y, and

f (0) = 3

f^{'} (0) = 3

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