1.

Given f(x) is a periodic function with period 2 and it is defined as ""f(x) = {{:([cos""(pix)/(2)]+1",",,0lt x lt 1), (2-x",",,1 le x lt 2):} Here [*] represents the greatest integer le x. If f(0)=1, then draw the graph of the function for x in [-2, 2].

Answer»

Solution :`f(x)= {{:([cos""(pix)/(2)]+1",",, 0 lt x lt 1), (2-x",",, 1 LE x lt 2):}`
`""= {{:(1",",, 0lt x lt 1), (2-x",",,1le x lt 2):}`

Since the function if periodic with period '2', the REQUIRED graph for `x in [-2, 1]` is as follows.


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