Question

Answer this ques with solution.
Chapter → Functions​

Answer 1

Answer:

Option"D" -f(x) is correct option

Step-by-step explanation:

Given :- f(x-y) = f(x)f(y) - f(a-x) f(a+y)

Let , x = 0 = y

• => f(0) = [f(0)]² - [f(a)]²

• => 1 = 1 - f(a)². [Given , f(0) =1 ]

• => f(a)² = 0

• => f(a) = 0 _____(1)

∴We have to find the value of f(2a-x)

• f(2a-x) = f{a-(x -a)}

• ∵ f(x-y) = f(x)f(y) - f(a-x)f(a+y)

• similarly, assume f(a-(x-a) , a as x and (a-x) as y

• then, f(2a-x) = f{a-(x-a)} = f(a)f{a-(x-a)} - f(a-a)f(a+x-a)

• => f(2a-x) = f(a)f(x-a) - f(a-a)f(x)

• f(2a-x) = 0 - f(x) ; [from given f(0)=1 and f(a) = 0 from 1st equation]

• ∴f(2a-x) = -f(x) Answer