f(x)=1/x*x*x range and domain
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MathBot Answer:
Range
Set notation:
\(\displaystyle\left\{f \in \mathbb{R}:f \neq 0\right\}\)
Interval notation:
\(\displaystyle\left(-\infty, 0\right) \cup \left(0, \infty\right)\)
Domain
Set notation:
\(\displaystyle\left\{x \in \mathbb{R}:x \neq 0\right\}\)
Interval notation:
\(\displaystyle\left(-\infty, 0\right) \cup \left(0, \infty\right)\)
\(\frac{x x}{x}\) has a removable singularity at \(x = 0\). A removable singularity of a function \(f\) is a point \(p\) at which \(f\) is undefined and where it is possible to redefine \(f\) such that the resulting function is continuous at \(p\). The resulting function is known as the continuous extension of \(f\) to \(p\).
The continuous extension of \(\frac{x x}{x}\) to \(0\) is:\[F(x) = \begin{cases} 0 & \text{for}\: x = 0 \\\frac{x x}{x} & \text{otherwise} \end{cases}\] The domain of \(F(x)\) is \(\Reals\) or \((-\infty, \infty)\).