Answer:



Explanation:
A piecewise function gives multiple sub-functions for different parts of its domain.
Given piecewise function:

Therefore, if x is less than or equal to zero, we should use f(x) = x² - 16.
Similarly, if x is greater than zero, we should use f(x) = 1 - 2x².

Part (a)
To find f(-4), substitute x = -4 into the function.
As -4 ≤ 0, use the first part of the function, f(x) = x² - 16.

Therefore:


Part (b)
To find f(0), substitute x = 0 into the function.
As 0 ≤ 0, use the first part of the function, f(x) = x² - 16.

Therefore:


Part (c)
To find f(5), substitute x = 5 into the function.
As 5 > 0, use the second part of the function, f(x) = 1 - 2x².

Therefore:
