Let a function `f(x)s a t i sfi e sf(x)+f(2x)+f(2-x)+f(1+x)=AAx in Rdot` Then find the value of `f(0)dot`

Explanation

`f(x) +f(2x)+f(2-x)+f(1+x)=x `
Put `x=0.` Then,
` f(0)+f(0)+f(2)+f(1)=0`
or `2f(0)+f(1)+f(2)=0 " (1)" `
Put `x=1`. Then,
`f(1)+f(2)+f(1)+f(2)=1`
` :. f(1)+f(2)=1//2`
So, from (1)
`2f(0)+1//2=0`
` :. f(0)= -1//4`