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If f(x) = {{:(x - [x]",",x !in I),(1",",...

If `f(x) = {{:(x - [x]",",x !in I),(1",",x in I):}` where I is an integer and [.] represents the greatest integer function and
`g(x) = lim_(n to oo) ({f(x)}^(2n)-1)/({f(x)}^(2n)+1)`, then
(a) Draw graphs of f(2x), g(x) and g{g(x)} and discuss their continuity.
(b) Find the domain and range of these functions.
(c) Are these functions periodic ? If yes, find their periods.

Text Solution

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The correct Answer is:
(a) `f(2x) = {{:(2x - [2x]",",2x !in I),(1",",2x in I):}`
(b) Domain of `g(g(x)) in R` and Range of `g(g(x)) in {0}`
(c) Here, f(2x) and g(x) are periodic with period 1/2 and 1 also g{g(x)} is constant function.
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