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Definition of Functions

22. A functio...

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22. A function f:R->R satisfies the following conditions: 1)f(x) not equal to zero , for all values of x corresponding to R 2)f(x+y) = f(x).f(y) , for all values of x & y corresponding to R 3)f(x) is differentiable 4)f'(0)=2 The value of f(0) is - A)1 B)-1 C)2 D)1/2

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f : R \to R

satisfies the equation

f (x + y) = f (x) f (y)

x, y \in R, f (x) \neq 0

. Suppose that the function is differentiable at

x = 0

f^{'} (0) = 2

f^{'} (x) = 2 f (x)

f : R \to R

be a differentiable function with

f (0) = 1

and satisfying the equation

f (x + y) = f (x) f^{'} (y) + f^{'} (x) f (y)

x, y \in R .

Then, the value of

{log}_{e} (f (4))

f : R \to R

is a differentiable function such that

f^{^{'}} (x) > 2 f (x)

x \in R

f (0) = 1

Q. Consider a real valued function

f : R \to R

f (\frac{2 x + 3 y}{5}) = \frac{2 f (x) + 3 f (y)}{5} \forall x, y \in R

f (0) = 2; f^{'} (0) = 1

Minimum distance of a point on graph of

y = f (x)

from origin is less than or equal to

f : R ⟶ R

satisfies the equation

f (x + y) = f (x), f (y)

x, y ϵ R, f (x) \neq 0

Suppose that the function is differentiable at x=0 and

f^{^{'}} (0) = 2

f^{^{'}} (x) = 2 f (x)

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