1.

Findf ( 2),if( ) 2 12f x  x  x  .

Answer»

ANSWER:

⇒F(X)+2f(1−x)=x2+2⋯⋯(i)

Put x=1−x

⇒f(1−x)+2f(x)=(1−x)2+2

Multiply by 2

⇒2f(1−x)+4f(x)=2(1−x)2+4⋯⋯(II)

Subtract (ii) from (i)

−3f(x)=x2−2−2(1−x)2

−3f(x)=x2−2−2x2+4x

−3f(x)=−(x2−4x+4)

f(x)=−3(x−2)2


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