函数的相关概念
换元
令t=(1-x)/(1+x)
(1+x)t=1-x
tx+x=1-t
x=(1-t)/(1+t)
f(t)
=(1-x²)/(1+x²)
=[1-(1-t)²/(1+t)²]/[1+(1-t)²/(1+t)²]
=[(1+t)²-(1-t)²]/[(1+t)²+(1-t)²]
=[(1+2t+t²)-(1-2t+t²)]/[(1+2t+t²)+(1-2t+t²)]
=(4t)/(2+2t²)
=2t/(1+t²)
将t换回x,即得
f(x)=2x/(1+x²)
高中函数概念
f(x)=5,说明函数是一条平行于x轴的直线,所以f(x^2)=5
举个简单的例子,由f(x)=5可知,在x=3和x=9时有f(3)=5,f(9)=5
那f(3^2)=f(9)=5