设f(x)为连续的偶函数,且当x>0时为单调函数,则满足f(x)=[(x+3)/(x+4)]的所有x的和为?务必要有详尽的解

Question

设f(x)为连续的偶函数,且当x>0时为单调函数,则满足f(x)=[(x+3)/(x+4)]的所有x的和为?务必要有详尽的解

Answer 1

f（x) = (x+3)/(x+4)
f(x) = f(-x)
(x+3)/(x+4) = (-x+3)/(-x+4)
(x+3)(-x+4) = (-x+3)(x+4)
-x^2+x+12 = -x^2-x+12
2x = 0
x = 0
所有x的和为 = 0