Let f (x) = 2mcos ^ 2x-2 √ 3msinx * cosx + n (M > 0) be defined as [0, Pai / 2] range [1,4] (1) (2) if f (x) = 2, find X

Let f (x) = 2mcos ^ 2x-2 √ 3msinx * cosx + n (M > 0) be defined as [0, Pai / 2] range [1,4] (1) (2) if f (x) = 2, find X

one
f(x)=2m(cosx)^2-m-3^0.5×2msinxconx+m+n
=mcos2x-3^0.5×msin2x+m+n
=2m(1/2×cos2x-3^0.5/2×sin2x)+m+n
=2mcos(π/3+2x)+m+n
x∈[0,π/2]
2x∈[0,π]
2x+π/3∈[π/3,4π/3]
cos(2x+π/3)∈[-1,1/2]
2mcos(π/3+2x)+m+n∈[-m+n,2m+n]
-m+n=1 2m+n=4
m=1 n=2
two
f(x)=2cos(2x+π/3)+3=2
cos(2x+π/3)=-1/2
2X + π / 3 = 2 π / 3 or 2x + π / 3 = 4 π / 3
X = π / 6 or x = π / 2

Given that f (x) is a quadratic function and f (x) + F (2x) = 5x2 + 3x + 2, find f (x)

Let f (x) = ax ^ 2 + BX + C. A ≠ 0
f(x) + f(2x)
= 5ax^2 + 3bx + 2c
= 5x^2 + 3x + 2
a = b = c = 1
f(x) = x^2 + x + 1