Question

已知f(2x-1)=x^2求f(x)表达式为

Answer 1

f(2x-1)=x²

令t=2x-1,则x=(t+1)/2

f(t)=x²=[(t+1)/2]²=(t²+2t+1)/4

f(t)=(t²+2t+1)/4即f(x)=(x²+2x+1)/4

f(x)表达式是f(x)=(x²+2x+1)/4