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if f(x) satisfies the relation 2f(x)+f(1-x)=x^2 for all real x, then find f(x).

if f(x) satisfies the relation 2f(x)+f(1-x)=x^2 for all real x, then find f(x).

Grade:12

1 Answers

suvidhi mehta
292 Points
3 years ago
2f(x)+f(1-x)=x^2 
this is a functional equality replace x by 1-x in whole equation
2f(1-x)+f(x)=(1-x)^2
now i think you can solve the above two equation to eliminate f(1-x) and get f(x)
i hope it helps you reach the answer

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