Final answer:
The piecewise function f(x) equals 6 when evaluated at x = -2, 8 when evaluated at x = 1, and 2 when evaluated at x = 2.
Step-by-step explanation:
The function f(x) provided here is a piecewise function where one function applies when x is less than 1, and a different function applies when x is 1 or greater:
- For x < 1: f(x) = -1x^2 + 10
- For x ≥1: f(x) = -2x^2 + 10
To calculate f(-2), we use the first function since -2 is less than 1:
f(-2) = -1(-2)^2 + 10 = -1(4) + 10 = -4 + 10 = 6
To calculate f(1), we use the second function since 1 is equal to 1:
f(1) = -2(1)^2 + 10 = -2(1) + 10 = -2 + 10 = 8
Finally, to calculate f(2), we again use the second function since 2 is greater than 1:
f(2) = -2(2)^2 + 10 = -2(4) + 10 = -8 + 10 = 2