The function \(f\) has domain \(\{x: -3< x <3, x \text{ is real}\}\) and is defined by
\[\begin{align*}
f:x\to -5-x, \qquad &(-3< x \le -1) \\
f: x\to 2x^3, \qquad&(-1< x \le 1) \\
f:x\to 5-x, \qquad &(1< x <3).
\end{align*}\]
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.
A relation is a set of pairs of values, where the order matters, for example, {(1,4), (2,8), (3,12)}.
You can see that this relation could be associated with the function \(f(x) = 4x\).
Can you give an example of a relation which cannot be associated with a function like this?
What is the property of a relation that makes it a function? Can you tell if the inverse you found for this question has this property?
