If f is an even function defined in the interval (-5,5), find four real values of x satisfying the equation `f(x)=f((x+1)/(x+2))`

Explanation

Since f is an even function, f(-x)=f(x).
`therefore` Now f((x+1)/(x+2))`=f(x) implies `f((x+1)/(x+2))`=f(-x)
This implies `(x+1)/(x+2)=x` or `(x+1)/(x+2)=-x`
`therefore x^2+x-1` or `x^2+3x+1=0`
`therefore x=(-1+-sqrt5)/2 or x=(-3+-sqrt5)/5`