differentiability

For the function f(x) = e⁻⁸|sin x|; x ∈ R, which of the following statements is/are TRUE?

For the function f(x) = e x |sin x|; x ∈ ℝ, which of the following statements is/are TRUE?

Let max {a, b} denote the maximum of two real numbers a and b. Which of the following statement(s) is/are TRUE about the function f(x) = max{3 - x, x - 1} ?

Let max {a, b} denote the maximum of two real numbers a and b. Which of the following statements is/are TRUE about the function f(x) = max{3 $$-$$ x, x $$-$$ 1}?

If $$y = \left| x \right|$$ for $$x < 0$$ and $$y=x$$ for $$x \ge 0$$ then

The function $$f\left( x \right) = \left| {x + 1} \right|$$ on the interval $$\left[ { - 2,0} \right]$$ is __________.