# A  real valued function satisfies the functional equation  where   is a given constant and   is equal to Option 1) Option 2) Option 3) Option 4)

As we learnt in

FUNCTIONS -

A relation f from a set A to a set B is said to be a function if every element of set A has one and only one image in set B.

-

f(x - y) = f(x) f(y) - f(a - x) f(a + y)                        (i)

f(0) =1,   f(2a - 2) = ?

Put x = y = 0

1 = | x | - f2(a)

f2(a) = 0    f(a) = 0

Now  f(2a - x) = f(a + a - x) = f(a - (x - a))

Where

f(a) f(x - a) - f(a - a) f(a + x - a) = 0 - 1  f(x) = - f(x)

Correct option is 2.

Option 1)

This is an incorrect option.

Option 2)

This is the correct option.

Option 3)

This is an incorrect option.

Option 4)

This is an incorrect option.

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