Consider the function `f(x)={{:(x-[x]-(1)/(2),x !in),(0, "x inI):}` where [.] denotes the fractional integral function and I is the set of integers. Then find `g(x)max.[x^(2),f(x),|x|},-2lexle2.`

Options

A. `A = (275)/(48)` sq. units
B. `A = (248)/(52)` sq. units
C. `g(x) {{:(x^(2),-2, le x lt - 1),(-x, -1,le x le - (1)/(4)),(x + (1)/(2), - (1)/(4) ,lt x le 0),(x, 0 ,lt x le 1),(x^(2), 1 ,lt x le 2):}`
D. `g(x) {{:(-x,-2 le x lt - 1),(x^(2), -1le x le - (1)/(4)),(x + (1)/(2), - (1)/(4) lt x le 0),(x^(2), 0 lt x le 1),(x, 1 lt x le 2):}`

Answer

A,C