+753 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)?
+129852
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
