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Consider the function f(x)={{:(x-[x]-(1)...

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.`

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):}`

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The correct Answer is:
A,C
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