From the lecture, we know that L{f(t)∗g(t)} ≠ L{f(t)}∗L{g(t)}. Show th

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From the lecture, we know that L{f(t)∗g(t)} ≠ L{f(t)}∗L{g(t)}. Show that this is false by providing a counter-example. In other words, find functions f(t) and g(t) such that L{f(t)∗g(t)} ≠ L{f(t)}∗L{g(t)} and demonstrate this by computing the left hand side and right hand side using those functions to show that they are indeed unequal.

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(2 points) From the lecture, we know that $L {f (t) * g (t)} \neq L {f (t)} *$ $L {g (t)}$ . Show that this is false by providing a counter-example. In other words, find functions $f (t)$ and $g (t)$ such that $L {f (t) * g (t)} \neq$ $L {f (t)} * L {g (t)}$ and demonstrate this by computing the left hand side and right hand side using those functions to show that they are indeed unequal.