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Suppose the function f(x) is defined explicitly by the table \(\begin{array}{c || c | c | c | c | c} x & 0 & 1 & 2 & 3 & 4 \\ \hline f(x) & 0 & 0 & 1 & 3 & 6 \end{array}\) This function is defined only for the values of x listed in the table. Suppose g(x) is defined as f(x)-x for all numbers x in the domain of f. How many distinct numbers are in the range of g(x)?

Lightning  Jul 21, 2018
 #1
avatar+87564 
+1

OK....

 

The integers in the domain of f(x)  are  0, 1, 2, 3, 4

 

So

g(0)  = f(0)  -  0    =  0  - 0  =  0 

g(1)   = f(1)  - 1  =  0 - 1  = -1

g(2)  = f(2)  - 2  = 1 - 2  = -1

g(3)  = f(3)  - 3  =  3 - 3  = 0

g(4)  = f(4)  - 4  =  6 - 4  = 2

 

So...the distinct numbers in the range of  g(x)  are  { -1, 0, 2 }  ⇒ i.e., three values

 

 

cool cool cool

CPhill  Jul 21, 2018

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