Limits Continuity And Differentiability

Let \(f:\left[ { - {1 \over 2},2} \right] \to R\) and \(g:\left[ { - {1 \over 2},2} \right] \to R\) be function defined by \(f(x) = [{x^2} - 3]\) and \(g(x) = |x|f(x) + |4x - 7|f(x)\), where [y] denotes the greatest integer less than or equal to y for \(y \in R\). Then