已知函数f(2x+1)=(2x+1)/(x+1),求函数f(x)

Question

已知函数f(2x+1)=(2x+1)/(x+1),求函数f(x)

Answer 1

f(2x+1)=(2x+1)/(x+1)
令2x+1=t ,x+1≠0,x≠-1
x=(t-1)/2
∴f(t)=f(2x+1)=(2x+1)/(x+1)
=t/[(t-1)/2+1]
=2t/(t+1)
∴f(x)=2x/(x+1) (x≠-1)