A real valued function satisfies the functional equation where is a given constant and is equal to
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.
Study 40% syllabus and score up to 100% marks in JEE