Suppose that the function g is defined, for all real numbers, as follows.=gx 2 ≤if x−2−+x122 <−if 2<x2+−14x1 ≥if x2Find g−5, g−2, and g−1.

Question

Suppose that the function g is defined, for all real numbers, as follows.

 g(x) =  
   2      if x ≤ -2 
  x - 2  if -2 &lt; x &lt; 1 
  2 + 14x if 1 ≤ x

Find g(-5), g(-2), and g(-1).

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Solution

The function g is defined in three parts, so we need to determine which part of the function to use for each value of x.

For g(-5), we use the first part of the function because -5 is less than 2. So, g(-5) = -5 + 2 = -3.
For g(-2), we use the second part of the function because -2 is equal to 2. So, g(-2) = -2^2 - 1 = -4 - 1 = -5.
For g(-1), we use the third part of the function because -1 is greater than 2. So, g(-1) = -1^2 = 1.

So, g(-5) = -3, g(-2) = -5, and g(-1) = 1.

This problem has been solved

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