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∵y=[1-√(1+4x)]/[1+√(1+4x)]
==>y+1=2/[1+√(1+4x)]
==>1+√(1+4x)=2/(y+1)
==>√(1+4x)=2/(y+1)-1
==>√(1+4x)=(1-y)/(y+1)
==>(1+4x)=(1-y)²/(y+1)²
==>4x=(1-y)²/(y+1)²-1
==>4x=-4y/(y+1)²
==>x=-y/(y+1)²
∴y=[1-√(1+4x)]/[1+√(1+4x)]的反函数是：y=-x/(x+1)².
==>y+1=2/[1+√(1+4x)]
==>1+√(1+4x)=2/(y+1)
==>√(1+4x)=2/(y+1)-1
==>√(1+4x)=(1-y)/(y+1)
==>(1+4x)=(1-y)²/(y+1)²
==>4x=(1-y)²/(y+1)²-1
==>4x=-4y/(y+1)²
==>x=-y/(y+1)²
∴y=[1-√(1+4x)]/[1+√(1+4x)]的反函数是：y=-x/(x+1)².
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