Question

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$g(t) = \

$$\begin{cases} -2t(t + 1) &, \\ t < 6 \\\\\\dfrac{5t}{6} &, \\ 6 \\leq t \\leq 12 \\\\2t^2 + 3t &, \\ t > 12 \\end{cases}$$

$
$g(12) = \square$
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worked example: evaluating piecewise functions

Explanation:

Step1: Identify correct function piece

For $t=12$, use $\frac{5t}{6}$ (since $6\leq t\leq12$)

Step2: Substitute $t=12$ into the function

$\frac{5\times12}{6}$

Step3: Calculate the result

$\frac{60}{6}=10$

Answer:

10