Question

一道数学题，会的帮下忙，急！！

注：(^2)就是平方，瞎担心下~

题：f(3x+1)=2x^2-3x-1
问：f(x)=____________

把步骤写得越详尽越好，最好要有原理。
豁出去了。。100分赏金！

Answer 1

f(3x+1)=2x^2-3x-1
设t=3x+1
x=(t-1)/3
f(t)=2[(t-1)^2/9]-(t-1)-1
=2(t-1)^2/9-t
=2t^2/9-4t/9+2/9-t
=2t^2/9+5t/9+2/9

Answer 2

设t=3x+1 则x=(t-1)/3
f(t)=2(t-1)^2/9-t
x代t f(x)=2(x-1)^2/9-x

Answer 3

3x+1=t
x=(t-1)/3

2[(t-1)/3]^2-3[(t-1)/3]-1

=2(t^2-2t+1)/9-(t-1)-1

=2t^2/9-4t/9+2/9-t+1-1

=2t^2-13t/9+2/9

f(x)=2x^2-13x/9+2/9

Answer 4

设t=3x+1
x=(t-1)/3
f(t)=2[(t-1)^2/9]-(t-1)-1
=2(t-1)^2/9-t
=2t^2/9-4t/9+2/9-t
=2t^2/9+5t/9+2/9
所以f(x)=2x^2/9+5x/9+2/9