Question

若函数f(x)的值域为闭区间1/2到3.求函数F(x)=f(x)+1/f(x)的值域

Answer 1

F(x)=f(x)+1/f(x)≥2

f(x)=1/2 F(x)=1/2+2=5/2

f(x)=3 F(x)=1/3+3=10/3

∴F(x)的值域为[2,10/3]