Question

Let $\Psi_{1}:[0, \infty) \rightarrow R, \Psi_{2}:[0, \infty) \rightarrow R, f:[0, \infty) \rightarrow R$ and $g:[0, \infty) \rightarrow R$ be functions such that $f (0)= g (0)=0$,
$\psi_{1}(x)=e^{-x}+x, x \geq 0,$
$\psi_{2}(x)=x^{2}-2 x-2 e^{-x}+2, x \geq 0,$
$f(x)=\int\limits_{-x}^{x}\left(|t|-t^{2}\right) e^{-t^{2}} d t$,$x > 0$
and g(x)=\int\limits_{0}^{x^{2}} \sqrt{t} e^{-t} d t, $$x > 0 .