SOLUTION: For all real numbers {{{x}}}, the function {{{f(x)}}} satisfies {{{2f(x) + f(1-x) = x^2}}} Find {{{f(5)}}}

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Question 252552: For all real numbers x, the function f%28x%29 satisfies 2f%28x%29+%2B+f%281-x%29+=+x%5E2
Find f%285%29
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
For all real numbers x, the function f%28x%29 satisfies 2f%28x%29+%2B+f%281-x%29+=+x%5E2
Find f%285%29

2f%28x%29%2Bf%281-x%29=x%5E2

Substitute x=5

2f%285%29%2Bf%281-5%29=5%5E2
2f%285%29%2Bf%28-4%29=25


Substitute x=-4

2f%28-4%29%2Bf%281-%28-4%29%29=%28-4%29%5E2
2f%28-4%29%2Bf%281%2B4%29=16
2f%28-4%29%2Bf%285%29=16

So we have this system of equations:

syatem%282f%285%29%2Bf%28-4%29=25%2C2f%28-4%29%2Bf%285%29=16%29

Solve that and get:
f%285%29=34%2F3 and f%28-4%29=7%2F3

Edwin