\[ T(v) = \begin{cases} 2v-1 & \text { if } -4 < v \leq -1 \\ -v+7 & \text { if } 1 \leq v < 7 \end{cases} \]
Graph of \(y = T(v)\).
![[Picture]](example_1-4d64a965c76bd43679c7dfe8ea1f9588.svg)
Define \(F\) as follows.
\[ F(x) = -x + 1 \, \text { with domain } \, [-3, 5] \]
![[Picture]](example_1-c4783920682b6ac336c8cf79d551ee64.svg)
To investigate the function \(T \circ F\) we need the range of \(F\) and the domain of \(T\).
The range of \(F\) is \(\left [ \answer {-4}, \answer {4} \right ]\).
The domain of \(T\) is \(\left ( \answer {-4}, \answer {1} \right ] \cup \left [ 1, 7 \right )\).
Their intersection is \(\left ( \answer {-4}, \answer {1} \right ] \cup \left [ 1, 4 \right ]\).