f(x)=(4cosx-5sinx)*cosx+cos2x/2
=4(cosx)^2-5sinxcosx+cos2x/2
=2(cos2x+1)-5six2x/2+cos2x/2
=5cos2x/2-5sin2x/2+2
=5根号2/2*cos(2x+π/4)+2,
因为x∈[0,π/2],
所以2x+π/4∈[π/4,5π/4],
所以cos(2x+π/4)∈[-1,根号2/2],
所以5根号2/2*cos(2x+π/4)∈[-5根号2/2,5/2],
所以f(x)∈[2-5根号2/2,9/2].
所以f(x)的值域为[2-5根号2/2,9/2].