Question

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

• A. f (x) = | x |
• B. f (x) = 2x
• C. f (x) = | x | + x
• D. f (x) = 2 | x |

Answer 1

Answer: (C)

f (x) = | x | + x

Answer 2

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