f(x)=1/2*(1+cos2x)/2 + √3/4*sin2x + 1=√3/4*sin2x + 1/4*cos2x + 5/4=1/2*sin(2x+30°）+ 5/4∵x∈[0,7π/12] ∴2x+30°∈[30°,240°] ∴sin(2x+30°）∈[-√3/2,1]∴f(x)∈[(5-√3)/4,7/4]