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General Tips for Choosing Function

16. A Functio...

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16. A Function F(x) satisfies the functional equation x F(x) + F(1-x) = 2x - x, for all real x. What should be F(x).

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Q. Let F(x) be an indefinite integral of

{sin}^{2} x .

STATEMENT-1 The function F(x) satisfies

F (x + π) = F (x)

for all real x. because STATEMENT-2:

{sin}^{2} (x + π) = {sin}^{2} x

for all real x.

f (x)

is a polynomial function satisfying the condition

f (x) \times f (\frac{1}{x}) = f (x) + f (\frac{1}{x})

f (2) = 9

Q. Let a function

f : R \to R

satisfy the equation

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

x, y

. If the function

f (x)

is continuous at

x = 0

y = f (x)

be a real-valued differentiable function on the set of all real numbers

R

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, then the area enclosed by

y = f (x)

x

-axis between ordinates

x = 0

x = 3

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be a function satisfying the condition

f (- x) = f (x)

x

f^{'} (0)

exists, then its value is

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