𝑔(𝑡)={2𝑡2+2𝑡−24𝑡−3𝑖𝑓 𝑡≠3𝑏𝑖𝑓 𝑡=3g(t)={ t−32t 2 +2t−24​ b​ if t≠3if t=3​ A.14B.3C.7D.None of theseE.0

It seems like there's a bit of confusion in your question as the function g(t) is defined twice with different expressions. However, if we're looking for the value of g(t) when t=3, we should use the second definition.

The second definition of g(t) is: g(t) = t - 3/2t^2 + 2t - 24

Let's substitute t=3 into this equation:

g(3) = 3 - 3/2*(3^2) + 23 - 24 = 3 - 3/29 + 6 - 24 = 3 - 13.5 + 6 - 24 = -28.5

So, the answer is not listed among the options you provided (A.14, B.3, C.7, D.None of these, E.0). The correct answer should be -28.5. Please check the question again.