证明：若f（x）=ax+b,则f((x1+x2)/2)={f(x1)+f(x2)}/2]

题目

证明：若f（x）=ax+b,则f((x1+x2)/2)={f(x1)+f(x2)}/2]

答案

f(x)=ax+b
f((x1+x2)/2)
=a((x1+x2)/2)+b
=ax1/2+ax2/2+b
[f(x1)+f(x2)]/2
=[ax1+b+ax2+b]/2
=ax1/2+ax2/2+b
所以
f((x1+x2)/2)=[f(x1)+f(x2)]/2