Question

设分段函数f(x)=(e^{2x}-1)/x,x>0;a,x=0;cosx+1,x<0;是连续函数,则a=_____

为什么是2

Answer 1

解f（-x）=（e^(-2x）-1/（e^(-2x）+1=(1-e^2x)/(1+e^2x)=-(e^2x-1)/(1+e^2x)=-f(x)故f(x)是奇函数令t=e^2x，则t＞0故原函数变为y=(t-1)/(t+1)=(t+1-2)/(t+1)=1-2/(t+1)由t＞0知t+1＞1则0＜1/(t+1)＜1则0＞-2/(t+1)＞-2则1＞1-2/(t+1)＞-1故-1＜y＜1故函数的值域为(-1,1).

Answer 2