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Grade: 11
        
A real valued functional equation f(x-y)=f(x)f(y)--(a-x)f(a+y), where is given constant and f(0)=1 then f(2a-x)=
7 months ago

Answers : (1)

Arun
20822 Points
							
Dear student
 
I have solved it in the following image, please check and in case of any difficulty please feel free to ask.
 
f(x-y) = f(x)f(y)-f(a-x)f(a+y)
y = 0
f(x-0) = f(x)f(0)-f(a-x)f(a+0)
f(0) = 1
f(x) = f(x)-f(a-x)f(a)
f(a-x)f(a) = 0
\Rightarrow f(a) = 0
f(2a-x) = f(a-(x-a)) = f(a)f(x-a)-f(a-a)f(a+x-a)f(2a-x) = f(a)f(x-a)-f(0)f(x)
f(a) = 0, f(0) = 1
f(2a-x) = -f(x)
7 months ago
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