+0  
 
+3
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avatar+332 

1. Let \(f(n) = \left\{ \begin{array}{cl} n^2-2 & \text{ if }n<0, \\ 2n-20 & \text{ if }n \geq 0. \end{array} \right.\)What is the positive difference between the two values of a that satisfy the equation f(-2)+f(2)+f(a)=0?

2. Let \(f(x) = \left\lceil\dfrac{1}{x+2}\right\rceil\) for x > -2, and \(f(x) = \left\lfloor\dfrac{1}{x+2}\right\rfloor\) for x < -2. (f(x) is not defined at x = -2.) Which integer is not in the range of f(x)?

MIRB16  Sep 3, 2017
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4+0 Answers

 #1
avatar+332 
+2

Also, thumbs up me!

MIRB16  Sep 3, 2017
 #2
avatar+76145 
+2

 

0  will not be in the range of either fiunction

 

The first one is a ceiling function....this means that it returns the least integer that is ≥ to f(x)

When   -2 < x < -1          the range is  [2, infinity )

When   x ≥ -1          the range is   1

 

The second is a floor function....this means that it returns the greatest integer ≤ to f(x)

When    -3 < x < -2    the range  is ( -infinity, -2 ]

When  x ≤ -3              the range is  -1

 

So......  the integer 0  is not in the range

 

 

cool cool cool

CPhill  Sep 3, 2017
 #3
avatar+332 
+3

Thanks CPhil!

MIRB16  Sep 3, 2017
edited by MIRB16  Sep 3, 2017
 #4
avatar+76145 
0

No prob  !!!!

 

 

cool cool cool

CPhill  Sep 3, 2017

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