Let f and g be differentiable function ...

Let `f and g` be differentiable function of R such that `g(x) leq 0, AA x in R` and Consider `h(x) = {f(x) for |f(x)| leq g(x) and g(x) for f(x) lt g(x) and -g(x) for f(x) lt -g(x)` which of the following statement is true for any `a in R?`

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