Question

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 1

$given \: \: f(x) + 2f(6 - x) = x \\ put \: \: x = 1 \\ f(1) + 2f(5) = 1 - - - (1)\\put \: \: x = 5 \\ f(5) + 2f(1) = 5 - - - (2) \\ 2 \times (2) - (1) \: \: gives \\ 4f(1) - f(1) = 5 \times 2 - 1 \\ 3f(1) = 9 \\ f(1) = 3$

Answer 2

Answer:

The value of f(1)=3.      

Step-by-step explanation:

Given : A certain function f satisfies the equation $f(x)+2\times f(6-x)=x$  for all real numbers x.

To find : The value of f(1) is?

Solution :

The given equation is $f(x)+2\times f(6-x)=x$

Put x=1,

$f(1)+2\times f(6-1)=1$

$f(1)+2\times f(5)=1$

$f(1)=1-2\times f(5)$

To find f(1) we have to find f(5),

So, Put x=5 in the equation,

$f(5)+2\times f(6-5)=5$

$f(5)+2\times f(1)=5$

$f(5)=5-2\times f(1)$

Put in f(1),

$f(1)=1-2\times (5-2\times f(1))$

$f(1)=1-10+4\times f(1)$

$f(1)=-9+4\times f(1)$

$3f(1)=9$

$f(1)=\frac{9}{3}$

$f(1)=3$

Therefore, The value of f(1)=3.