Suppose g is function such that 2gx gx2 gx and g02 Calcula

Solution

2g\'(x) /[ g(x) (g(x) + 2) ] = 1

g\'(x)/g(x) - g\'(x)/( g(x) + 2) = 1

integrate

ln g(x) - ln[ g(x) +2 ] = x + c

when x=0, g(x) = 2

ln 2 - ln 4 = 0 + c

c = -ln 2

put x=2

ln [ g(2)/(g(2) + 2) ] = 2 + c

= 2- ln2 = 1.307