$4\mathrm{.}19.$ Consider a causal LTI system with frequency response

H$($j$\backslash$omega $)=(1)/($j$\backslash$omega $+3).$

For a particular input x$($t$)$ this system is observed to produce the output

y$($t$)=$e$^(-3$t$)$u$($t$)-$e$^(-4$t$)$u$($t$).$