Chapter 10.1, Problem 5TFR

For Questions (a)-(i), decide if the given statement is true or false, and give a brief justification for your answer. If true, you can quote a relevant definition or theorem from the text. If false, provide an example, illustration, or brief explanation of why the statement is false.

The Laplace transform of a function $f$ is a function $F\left(s\right)$ defined by

$F\left(s\right)={\displaystyle {\int }_1^{\infty }{e}^{-st}f\left(t\right)}dt$,

provided that this improper integral converges.