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
a) 2
b) can't determine
c) 1
d) 3

• f(1)+2*f(6-1)=1......... (1)
  f(5)+2*f(6-5)=5......... (2)
  substituting we have (2) in (1) we have :-
  -3f(1)=-9,
  hence answer f(1)=3.
  
• 9 years agoHelpfull: Yes(28) No(1)
• f(1)+2f(5)=1------ (1)
  f(5)+2f(1)=5........*2
  => 2f(5)+4f(1)=10-------- (2)
  (2)-(1)
  => 3f(1)=9
  f(1)=3 (d)
• 9 years agoHelpfull: Yes(3) No(0)
• why f(5) was taken????????
• 6 years agoHelpfull: Yes(3) No(0)
• f(1)+2*f(6-1)=1
  or,f(1)+2*f(5)=1......... (1)
  
  f(5)+2*f(6-5)=5
  or,f(5)+2*f(1)=5......... (2)
  
  equating these two eqn.s we get, 3 f(1) = 9, therefore f(1) =3
• 9 years agoHelpfull: Yes(2) No(0)
• first put x=1 and make a equation like that f(1)+2*f(5)=1......................1
  now put x=5 in main equation so 2*f(1)+f(5)=5.......................2
  and solve thes both equ. find f(1)=3
  SHANU CHAUHAN IEC
• 9 years agoHelpfull: Yes(2) No(0)
• answer is 3
• 9 years agoHelpfull: Yes(0) No(0)
• f(1) = 3
  after solving two equation
  1 putting x = 1
  another putting x = 5
• 9 years agoHelpfull: Yes(0) No(0)
• answer is 3
• 9 years agoHelpfull: Yes(0) No(0)
• d) 3
  f(1)+2f(5)=1
  f(5)=5-2*f(1)
  by putting the value of f(5)
  f(1)=3
• 9 years agoHelpfull: Yes(0) No(0)
• d is correct ans
  f(1)+2*f(6-1)=1----1
  f(5)+2*f(6-5)=5-----2
  subsituting we have 2 and 1
  -3f(1)=-9
  hence ans f(1)=3
• 9 years agoHelpfull: Yes(0) No(0)
• answer is 3
• 9 years agoHelpfull: Yes(0) No(0)
• f(x)+2*f(6-x)=x...(1)
  f(6-x)+2*f(6-(6-x))=6-x => f(6-x)+2*f(x)=6-x....(2)
  equating those,we get f(x)=4-x.....
  f(1)=4-1=3
• 9 years agoHelpfull: Yes(0) No(0)
• f(1)+2f(5)=1
  f(5)+2f(1)=5
  after solving two equation
  f(1)=3
  answer is 3
• 9 years agoHelpfull: Yes(0) No(0)
• put x=1 then get f(1)+2*f(5)=1 ---------->1
  put x=5 then get f(5)+2*f(1)=5------------>2
  from egn(1)we take
  f(5)=1-f(1)/2
  then substitute 1 in 2
  1-f(1)+2*f(1)=5
  f(1)=3
  
  
• 8 years agoHelpfull: Yes(0) No(0)
• why f(5) is taken?
• 7 years agoHelpfull: Yes(0) No(0)
• f(x)+2*f(6-x)=x. Putting 6-x in place of x, we get f(6-x)+2*f(x)=6-x.
  Solving we get, f(x)=4-x.
  Putting x=1, f(1)=4-1=3.
• 7 years agoHelpfull: Yes(0) No(0)