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Define g(x) as follows:                                  

 

            \( g(x)= \begin{cases} -1, & \text{if } x < 0,\\ 0, & \text{if } x = 0, \\ 1, & \text{if } x > 0. \\ \end{cases} \)  

 

Let f(x) = g(x+1) - g(x-1). Compute f(1/2) + f(-1/2).

 Sep 18, 2019
 #1
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f(x) = g(x+1) - g(x-1)

f(1/2) = g (1 1/2) - g (-1/2)

         =    1 - -1 = 2

 

f(-1/2) = g(-1/2 + 1) - g(-1/2-1)

            = g(1/2) - g(-1 1/2)

            =    1      -   -1  = 2

 

f(1/2) + f(-1/2) = 2 + 2  = 4 

 Sep 18, 2019

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