galaxylee 寫到:
3.函數f(x)為實變數函數,若對任意實數a,b,f(a+b)=f(ab)且f(1/2)= -1/2,求f(x)
既a,b可為任意數,可先令a=0,所以左式f(a+b)=f(b),右式f(ab)=f(0)
所以存在無限組實數代入,其值皆為f(0)
又a=0,b=1/2時,原式為f(1/2)=f(0)=-1/2
故唯一解必為f(x)=-1/2
galaxylee 寫到:
3.函數f(x)為實變數函數,若對任意實數a,b,f(a+b)=f(ab)且f(1/2)= -1/2,求f(x)
galaxylee 寫到:1.試求多項式p(x),使其滿足p(x^2+1)=(p(x))^2 + 1,且p(0)=0