Function f satisfies the equation f(x)+2*f(6-x)=x for all real numbers x. Find the value of f(1)

• let x=1 then, f(1)+2f(5)=1-------(1)
  let x=5 then, f(5)+2f(1)=5-------(2)
  from (2) f(5)=5-2f(1) sub in (1)
  f(1)+2(5-2f(1))=1
  f(1)+10-4f(1)=1
  -3f(1)=-9
  f(1)=3
  ans=3
• 9 years agoHelpfull: Yes(11) No(0)
• first put the value of x=1
  then we will get equation in terms of f(5) as f(1)+2*f(5)=1
  then put x=5 f(5)+2*f(1)=5
  multiply second equation with 2we will get 2*f(5)+4*f(1)=10
  substracting the equation we get 3*f(1)=9
  so f(1)=3
  
• 9 years agoHelpfull: Yes(2) No(0)
• f(1)+2f(5)=1
  f(5)+2f(1)=5
  f(5)=5-2f(1)
  =>f(1)+2{5-2f(1)}=1
  f(1)=3
• 9 years agoHelpfull: Yes(0) No(0)
• ans f(1) is 3
• 9 years agoHelpfull: Yes(0) No(0)