Given:
a function is given as below
Find:
we have to find the value of f(t + 2), when t = 2.
Explanation:
Firstly we will find f(t + 2) as following
[tex]\begin{gathered} f(t+2)=\begin{cases}{-2(t+2)-3\text{ ,if t + 2 < 3}} \\ {} \\ {(t+2)^2-2(t+2),\text{ if t + 2 }\ge\text{ 3}}\end{cases} \\ f(t+2)=\begin{cases}{-2t-7,\text{ if t < 1}} \\ {} \\ {t^2+2t,\text{ if t }\ge\text{ 1}}\end{cases} \end{gathered}[/tex]
when t = 2,
we have, f(t + 2) = t² + 2t
f( 2 + 2) = (2)²+2(2) = 4 + 4 = 8
Therefore, the value of f(t + 2) ,when t = 2 is 8.
