Suppose that the function h is defined, for all real numbers, as follows.=hx −14x2    ≤if x−2−+x12    <−if 2≤x2−3    >if x2Find h−2, h1, and h5.

The function h is defined in three parts. Let's find the values step by step:

1. For h(-2), we look at the first condition x ≤ -2. Since -2 is equal to -2, we use the first equation -14x^2. Substituting x with -2, we get h(-2) = -14*(-2)^2 = -14*4 = -56.

2. For h(1), we look at the second condition -2 < x < 2. Since 1 is within this range, we use the second equation -x + 12. Substituting x with 1, we get h(1) = -1 + 12 = 11.

3. For h(5), we look at the third condition x ≥ 2. Since 5 is greater than 2, we use the third equation 2 - 3. This equation does not depend on x, so h(5) = 2 - 3 = -1.

So, h(-2) = -56, h(1) = 11, and h(5) = -1.