Let y 1 : [0, ∞) R , y 2 : [0, ∞ ] R , f : [0, ∞) R , and g : [0, ∞] R , be functions…

Let y₁ : [0, ∞) \(\rightarrow \mathbb{R},\)
y₂ : [0, ∞] \(\rightarrow \mathbb{R},\) f : [0, ∞) \(\rightarrow \mathbb{R},\) and g : [0, ∞] \(\rightarrow \mathbb{R},\) be functions such that f(0) = g(0) = 0, y₁(x) = e^–x + x, x ≥ 0, y₂(x) =
x² – 2x – 2e^–x + 2, x ≥ 0, \(f(x)=\int_{-x}^{x}\left(|t|-t^{2}\right) e^{-t^{2}} d t, x>0\) and \(g(x)=\int_{0}^{x^{2}} \sqrt{t} e^{-t} d t, x>0\)

Which of the following statements is TRUE?