Question

已知函数f(x)的定义域是R,函数g(x)=f(x)+f(-x),若g(x)在(0,+∞)上是增函数,且a =g(-1),b=g(-2),c=g(-1/2),

则abc的大小关系是

Answer 1

∵g(-x)=g(x)
函数g(x)=f(x)+f(-x)为偶函数
a =g(-1)=g(1),b=g(-2)=g(2),c=g(-1/2)=g(1/2),
g(x)在(0,+∞)上是增函数∵1/2<1<2∴c<a<b

Answer 2

g(-x)=g(x)
函数g(x)=f(x)+f(-x)为偶
a =g(-1)=g(1),b=g(-2)=g(2),c=g(-1/2)=g(1/2),
g(x)在(0,+∞)上是函数∵1/2<1<2∴c<a<b
(x)在(0,+∞)上是增函数，
-2《-1〈-1/2
a<b<c

Answer 3

g(x)在(0,+∞)上是增函数，
-2《-1〈-1/2
a<b<c