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`        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)=`
11 months ago

Arun
22576 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)$
```
11 months ago
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### Course Features

• 731 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions