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

Question

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

Answer 1

左端=a*[(x1+x2)/2]+b=(ax1+ax2+2b)/2
右端=[(ax1+b)+(ax2+b)]/2=(ax1+ax2+2b)/2
左端=右端,所以原式成立.