Step-by-step explanation:
f(x) is a generic function definition. a kind of recipe that has to be applied when an actual number is given for the function, or when we use it to combine in another generic function.
whatever we use for the function parameter (either a specific number or another generic expression) we have then use at every location of x in the original f(x) definition. and then simplify or outright calculate.
in our case here we get specific numbers.
f(-4) means we need to place -4 into every location of x.
-4 < -1 true
so, we have to use
(1/2)x - 2
(1/2)(-4) - 2 = -4/2 - 2 = -2 - 2 = -4 = -4/1
f(1) means we need to place 1 into every location of x.
-1 <= 1 < 2 true
(x + 1)² - 3
(1 + 1)² - 3 = 2² - 3 = 4 - 3 = 1 = 1/1
f(2) means we need to place 2 into every location of x.
2 >= 2 true (2 < 2 is false !!!)
1
f(2) = 1 = 1/1
