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Section 8.3 Functions Defined on Intervals
We know turn to defining a function on an interval. It is natural to define
\begin{equation*}
f(\boldsymbol{x}) = \{ y \; | \; y=f(x), x \in \boldsymbol{x}\}
\end{equation*}
where \(\boldsymbol{x}\) is an interval as defined in this chapter. In many cases, this is well-defined.
Example 8.3.1.
Let
\(A=[-1,1]\text{,}\) \(B=[0,\pi]\) and
\(C=[1,9]\text{.}\) Then
\begin{align*}
e^A \amp = [e^{-1},e] \\
\sin(B) \amp = [0,1]\\
\sqrt{C} \amp = [1,3]
\end{align*}
