Question

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$f(t) = \

$$\begin{cases} -\\dfrac{64}{t} &, \\ t = 8 \\\\ 14 - t &, \\ t = 10 \\\\ t^2 - 3t + 2 &, \\ t \ eq 8,10 \\end{cases}$$

$
$f(2) = \square$
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worked example: evaluating piecewise functions

Explanation:

Step1: Determine the applicable function

Since \( t = 2 \), and \( 2
eq8,10 \), we use the function \( f(t)=t^{2}-3t + 2 \).

Step2: Substitute \( t = 2 \) into the function

Substitute \( t = 2 \) into \( t^{2}-3t + 2 \):
\[

$$\begin{align*} f(2)&=2^{2}-3\times2 + 2\\ &=4-6 + 2\\ &=0 \end{align*}$$

\]

Answer:

\( 0 \)