Question:

What is the equivalent definition of the function given by $f(X) = \begin{cases} 2x , & x \ge 0 \\ 0,& x < 0 \end{cases} $ ?

Updated On: Jul 7, 2022
  • f (x) = | x |
  • f (x) = 2x
  • f (x) = | x | + x
  • f (x) = 2 | x |
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The Correct Option is C

Solution and Explanation

The given function is $f(x) = \begin{cases} 2x , & x \ge 0 \\ 0,& x < 0 \end{cases} $ The equation can be re-written as $f(x) = \begin{cases} x + x , & x \ge 0 \\ -x + x ,& x < 0 \end{cases} $ Hence, equivalent definition of given function is f (x) = | x | + x
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