求一道英文数学题!consider the linear function f(x)=ax+b.compute all order_数学解答

求一道英文数学题!
consider the linear function f(x)=ax+b.compute all ordered pairs (a,b) such that for all real numbers x,f(f(x))+f(x)=6x+60.

人气：345 ℃　时间：2020-03-22 08:21:32

解答

呵呵,直接代入啊...f(f(x))=a(ax+b)+b=a^2x+ab+b.f(f(x))+f(x)=a^2x+ax+ab+2b...要满足在任意情况下都等于右边6x+60.则对应的系数要相等哦,对应项的.a^2+a=6.a=2 或 a=-3ab+2b=60 当a=2时,b=15..当a=-3时,b=-60.....