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  • For x belong , the function f(x) satisfies 2f(x)+f(1-x)=x^2 Then , the value of f(4) is equal to

For x belong , the function f(x) satisfies 2f(x)+f(1-x)=x^2 Then , the value of f(4) is equal to

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Solution: If we observe the given equation , then f(x) and f(1-x) are

used ie, x is to be replaced by (1-x).

\ herefore 2f(x)+f(1-x)=x^2 .............(1) imes 2\ \Rightarrow 2f(1-x)+f(x)=(1-x)^2 .....................(2)\ \Rightarrow 3f(x)=2x^2-(1-x)^2\ \Rightarrow f(x)=1/3[x^2+2x-1]\ \Rightarrow f(4)=1/3[16+8-1]=23/3

Posted by

Deependra Verma

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