Answer:
- f(-5) = 3
- f(-2) = -9
- f(1) = 0
Explanation:
You have a piecewise defined function f(x) and you want the values of f(-5), f(-2), and f(1).
The first step in finding the value of a piecewise defined function is to determine the function definition on the domain containing the x-value of interest.
F(-5)
The value x=-5 is in the interval x < -2, so the first part of the function definition applies: f(x) = 3.
f(-5) = 3
F(-2)
The value x = -2 is in the interval -2 ≤ x ≤ 2, so the second part of the function definition applies: f(x) = -(x -1)².
f(-2) = -(-2 -1)² = -(-3)²
f(-2) = -9
F(1)
The value x = 1 is in the interval -2 ≤ x ≤ 2, so the second part of the function definition applies: f(x) = -(x -1)².
f(1) = -(1 -1)² = -(0)²
f(1) = 0