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A Certain Function F Satisfies The Equation F(x)+2*f(6-x)=x For All Real Numbers X. The Value Of F(1) Is? |
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Answer» PUT x =1 ⇒ F(1)+2*f(6-1) = 1 ⇒ f(1) + 2*f(5) = 1 Put x = 5 ⇒ f(5)+2*f(6-5) = 5 ⇒ f(5) + 2*f(1) = 5 Put f(5) = 5 - 2*f(1) in the first equation ⇒ f(1) + 2*(5 - 2*f(1)) = 1 ⇒ f(1) + 10 - 4f(1) = 1 ⇒ f(1) = 3. Put x =1 ⇒ f(1)+2*f(6-1) = 1 ⇒ f(1) + 2*f(5) = 1 Put x = 5 ⇒ f(5)+2*f(6-5) = 5 ⇒ f(5) + 2*f(1) = 5 Put f(5) = 5 - 2*f(1) in the first equation ⇒ f(1) + 2*(5 - 2*f(1)) = 1 ⇒ f(1) + 10 - 4f(1) = 1 ⇒ f(1) = 3. |
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