State the range of the function and sketch the graph of \(y=f(x)\). Define the inverse relation in similar form and determine whether this inverse relation is a function.
Combining Functions
Question
The function \(f\) has domain \(\{x: -3< x <3, x \text{ is real}\}\) and is defined by
\[\begin{align*}
f:x\to -5-x, \qquad &(-3< x \le -1) \\
f:x\to 2x^3, \qquad &(-1< x \le 1) \\
f:x\to 5-x, \qquad &(1< x <3).
\end{align*}\]
