Latest TCS Aptitude Question SOLUTION: Function f satisfies the equation f(x)+2*f(6-x)=x for all real numbers x. Find the value of f(1)

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

Asked In TCS Nakshatra Mukhopadhyay (8 years ago)

Unsolved Read Solution (4)

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raghavendra  (8 years ago)

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

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sanjeev  (8 years ago)

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

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Kadir ali  (8 years ago)

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

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ABHINAV  (8 years ago)

ans f(1) is 3

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