If f (x) = sin (2x + Pai / 3), then () A. The image of F (x) is symmetric with respect to the line x = Pai / 3 B. The image of F (x) is symmetric with respect to (PAI / 4,0) C. The image of F (x) is shifted to the left by Pai / 12 units to obtain the image of an even function D. The minimum positive period of F (x) is Pai and is an increasing function on [0, Pai / 6]

If f (x) = sin (2x + Pai / 3), then () A. The image of F (x) is symmetric with respect to the line x = Pai / 3 B. The image of F (x) is symmetric with respect to (PAI / 4,0) C. The image of F (x) is shifted to the left by Pai / 12 units to obtain the image of an even function D. The minimum positive period of F (x) is Pai and is an increasing function on [0, Pai / 6]

A wrong
The symmetry axis of F (x) is taken at the extreme value
B wrong
The symmetry point of F (x) is at 0
C yes!
If the image of F (x) is shifted to the left by Pai / 12 units, then:
The new function is:
Sin [2 (x + π / 12) + π / 3] = sin (2x + π / 2), even function!
D wrong
The minimum positive period of F (x) is π
But it's not monotonous on [0, Pai / 6]!
[option C]