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What is the equivalent definition of the function given by
$\mathrm{f}(\mathrm{x})=\left\{\begin{array}{l}2 \mathrm{x}, \mathrm{x} \geq 0 \\ 0, \mathrm{x} < 0\end{array} ?\right.$
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$\mathrm{f}(\mathrm{x})=\left\{\begin{array}{l}2 \mathrm{x}, \mathrm{x} \geq 0 \\ 0, \mathrm{x} < 0\end{array} ?\right.$
Solution:
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Verified Answer
The correct answer is:
$\mathrm{f}(\mathrm{x})=|\mathrm{x}|+\mathrm{x}$
The given function is $\mathrm{f}(\mathrm{x})=\left\{\begin{array}{l}2 \mathrm{x}, \mathrm{x} \geq 0 \\ 0, \mathrm{x} < 0\end{array}\right.$
The equation can be re-written as
$f(x)=\left\{\begin{array}{ll}x+x, & x \geq 0 \\ -x+x & x < 0\end{array}\right.$
Hence, equivalent definition of given function is $\mathrm{f}(\mathrm{x})=|\mathrm{x}|+\mathrm{x}$
The equation can be re-written as
$f(x)=\left\{\begin{array}{ll}x+x, & x \geq 0 \\ -x+x & x < 0\end{array}\right.$
Hence, equivalent definition of given function is $\mathrm{f}(\mathrm{x})=|\mathrm{x}|+\mathrm{x}$
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