f(X)=(1/2)(2X-1+1)+4/(2X-1)
=(1/2)(2X-1)+4/(2X-1)+1/2
∵X＞1/2∴2X-1＞0
∴f（x）≥2√[（1/2）×4]+1/2=2√2+(1/2)
当且仅当(1/2)(2X-1)=4/(2X-1)时取“=”
故f（x）min=2√2+(1/2)
f(X)=(1/2)(2X-1+1)+4/(2X-1)
=(1/2)(2X-1)+4/(2X-1)+1/2
∵X＞1/2∴2X-1＞0
∴f（x）≥2√[（1/2）×4]+1/2=2√2+(1/2)
当且仅当(1/2)(2X-1)=4/(2X-1)时取“=”
故f（x）min=2√2+(1/2)