问题 选择题 函数y=1+2x1-2x(x∈R,且x≠-12)的反函数是( )A.y=1+2x1-2x(x∈R,且x≠12)B.y=1-2x1+2x(x∈R,且x≠-12)C.y=1+x2(1-x)(x∈R,且x≠-1)D.y=x-12(1+x)(x∈R,且x≠-1) 答案 由y=1+2x1-2x,得x=y-12(y+1),∴原函数的反函数是y=x-12(x+1)(x∈R,且x≠-1).故选D.