first find domian and square the function
u will get minimum value root3, to find maximum put x =1.5 u will get answer..
Hence ans would be (D)
One way to do this is is to let x^2 = 4 \cos^2 \theta+\sin^2 \theta
The expression reduces to \sqrt 3 \left(|\cos \theta| + |\sin \theta| \right)
We have 1 \le |\cos \theta| + |\sin \theta| \le \sqrt 2
Hence the range is [\sqrt 3, \sqrt 6]