If `f`is an even function defined on the interval `(-5,5),`then four real values of `x`satisfying the equation `f(x)=f((x+1)/(x+2))`are ______, __________, _______ and______.

If `f`is an even function defined on the interval `(-5,5),`then four r

1.	If `f`is an even function defined on the interval `(-5,5),`then four real values of `x`satisfying the equation `f(x)=f((x+1)/(x+2))`are ______, __________, _______ and______.
Answer» Correct Answer - `((pm3 pm sqrt(5))/(2))` Since, f is an even function, then `f(-x)=f(x), AA x in (-5,5)` Given, `f(x)=f((x+1)/(x+2)) " ...(i)" ` `rArr f(-x)=f((-x+1)/(-x+2))` `rArr f(x)=f((-x+1)/(-x+2))" "[ because f(-x)=f(x)]` Talking `f^(-1)` on both sides, we get `x=(-x+1)/(-x+2)` `rArr -x^(2)+2x= -x+1` `rArr x^(2)-3x+1=0` `rArr x=(3pm sqrt(9-4))/(2)=(3pm sqrt(5))/(2)` Again, `f(x)=f((x+1)/(x+2))` `rArr f(-x)=f((x+1)/(x+2)) " "[because f(-x)=f(x)]` Taking `f^(-1)` on both sides, we get `-x=(x+1)/(x+2)` `rArr x^(2)+3x+1=0` `rArr x=(-3 pm sqrt(9-4))/(2)=(-3pm sqrt(5))/(2)` Therefore, four values of x are `(pm 3pm sqrt(5))/(2)`