Write the piecewise function in terms of unit step functions

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Write the piecewise function

$f(t) = \begin{cases} 2t, & 0\leq t < 3 \\ 6, & 3 \le t < 5 \\ 2t, & t \ge 5 \\ \end{cases} $

in terms of unit step functions.

So here is what i;ve got just guessing , I don't think i'm correct. I really need some help. But I got:

$f(t) = 2t[u(t-0) - u(t-3)] + 6[u(t-3) - u(t-5)] + 2t[u(t-5) - u(t - \infty)]$

Which becomes

$f(t) = 2t[u(t) - u(t-3)] + 6[u(t-3) - u(t-5)] + 2t[u(t-5)]$

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1 Answer

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Solution is correct, verified by teacher.

$f(t) = 2t[u(t) - u(t-3)] + 6[u(t-3) - u(t-5)] + 2t[u(t-5)]$

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