已知函数f(x)=In(eX+1)+ax为偶函数,则a=? (x为次方)
f(x)=In(eX+1)+ax....................(1)
f(-x)=ln[e^(-x)+1]-ax=ln[(1+e^x)/e^x]-ax
=ln(e^x+1)-x-ax.....................(2)
f(x)=In(eX+1)+ax为偶函数:f(-x)=f(x):(1)=(2)
ax=-x-ax,2ax=-x,∴a=-1/2
f(x)=In(eX+1)+ax....................(1)
f(-x)=ln[e^(-x)+1]-ax=ln[(1+e^x)/e^x]-ax
=ln(e^x+1)-x-ax.....................(2)
f(x)=In(eX+1)+ax为偶函数:f(-x)=f(x):(1)=(2)
ax=-x-ax,2ax=-x,∴a=-1/2