Question

高一数学求函数解析式已知f（1-2x）=x平方分之（1-x平方）,求f（x）解析式

Answer 1

f(1-2x)=(1-x²)/x²

=1/x²-1

令z=1-2x

2x=1-z

x=(1-z)/2

f(z)=1/((1-z)/2)²-1

=4/(1-2z+z²)-1

=(4-(1-2z+z²))/(1-2z+z²)

=(3+2z-z²)/(1-2z+z²)

即：f(x)=(3+2x-x²)/(1-2x+x²)