CUET Preparation Today
A real valued function f(x) satisfies the functional equation $f(x - y) = f(x) f(y) - f(a - x) f(a + y)$ where a is a given constant and $f(0) = 1, f(2a - x)$ is equal to: |
$-f(x)$ $f(x)$ $f(a) + f(a - x)$ $f(-x)$ |
$-f(x)$ |
$f(a-(x-a))=f(a)-f(0)f(x)$ $=-f(x)[∵x=0,y=0,f(0)=f^1(0)-f^2(a)=0⇒f(a)=0]$ |
