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Question: Answered & Verified by Expert
What is the equivalent definition of the function given by
$\mathrm{f}(\mathrm{x})=\left\{\begin{array}{l}2 \mathrm{x}, \mathrm{x} \geq 0 \\ 0, \mathrm{x} < 0\end{array} ?\right.$
MathematicsFunctionsNDANDA 2006 (Phase 2)
Options:
  • A $\mathrm{f}(\mathrm{x})=|\mathrm{x}|$
  • B $\mathrm{f}(\mathrm{x})=2 \mathrm{x}$
  • C $\mathrm{f}(\mathrm{x})=|\mathrm{x}|+\mathrm{x}$
  • D $\mathrm{f}(\mathrm{x})=2|\mathrm{x}|$
Solution:
1767 Upvotes 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 $\mathrm{f}(\mathrm{x})=|\mathrm{x}|+\mathrm{x}$

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