Question 41

Let the functions $$f:(-1, 1) \rightarrow R$$ and $$g:(-1, 1) \rightarrow (-1, 1)$$ be defined by
$$f(x) = \mid 2x - 1 \mid + \mid 2x + 1 \mid$$ and $$g(x) = x - [x]$$,
where $$[x]$$ denotes the greatest integer less than or equal to ๐‘ฅ. Let $$f \circ g :(โˆ’1, 1) \rightarrow R$$ be the composite function defined by $$(f \circ g)(x) = f(g(x))$$. Suppose c is the number of points in the interval (-1, 1) at which $$f \circ g$$ is NOT continuous, and suppose d is the number of points in the interval(-1, 1) at which $$f \circ g$$ is NOT differenciable. Then the value of c + d is ____________


Correct Answer: e


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