1.

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?

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.



Discussion

No Comment Found

Related InterviewSolutions