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  • If f(x^2-6x+6)+f(x^2-4x+4) =2x for all x belong to R then f(-3)+f(9)-5f(1)=?

If f(x^2-6x+6)+f(x^2-4x+4) =2x for all x belong to R then f(-3)+f(9)-5f(1)=?

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Solution: \ x^2-6x+6=x^2-4x+4Rightarrow x=1

Put x=1 in the given relation to get

f(1)=1

for x^2-6x+6=1Rightarrow x=1,5

for x^2-4x+4=1Rightarrow x=1,3

Put x=3 and 5in the given relation to get

f(-3)+f(1)=6Rightarrow f(-3)=5\ \Rightarrow f(1)+f(9)=10Rightarrow f(9)=9\ \ herefore f(-3)+f(9)-5f(1)=9

 

Posted by

Deependra Verma

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