已知函数f(x-1)=x^2,求f(x)

2024-11-23 02:52:12
推荐回答(3个)
回答1:

f(x-1)=x^2,注意自变量是x-1,函数表达式中只能出现x-1形式
f(x-1)=x^2=(x-1+1)²=(x-1)²+2(x-1)+1
即f(x)=x^2+2x+1

回答2:

令t=x-1 则f(x-1)=f(t) x=t+1 x^2=(t+1)^2 所以f(t)=(t+1)^2 即f(x)=(x+1)^2

回答3:

f(x-1)=x²
=x²-2x+1+2x-1
=(x-1)²+2x-2+1
=(x-1)²+2(x-1)+1