a) f(-5) = 27
b) f(-1) = 7
c) f(2) = 4
d) f(5) = 10
e) f(9) = 48
Explanation:a) To get f(-5), we will check the intervals in the piece-wise function.
-5 is less than 0
The interval where -5 belongs is x ≤0
We will substitute x for -5 in the function with interval x ≤ 0
[tex]\begin{gathered} f(x)\text{ = 2 - 5x} \\ f(-5_{})\text{ = 2 - 5(-5)} \\ f(-5)\text{ = 2 + 25} \\ f(-5)\text{ = 27} \end{gathered}[/tex]b) f(-1): To get f(-1), we will check the interval which has x = -1
The interval where -1 belongs is x ≤0
[tex]\begin{gathered} \text{function for }x\le0\text{ is f(x) = 2 - 5x} \\ f(-1)\text{ = 2 - 5(-1)} \\ f(-1)\text{ = 2 + 5 = 7} \end{gathered}[/tex]c) f(2): To get f(2), we will check the interval which has x = 2
The interval where 2 belongs is 0 < x < 9
[tex]\begin{gathered} \text{function for }0d) f(5): we will check the interval which has x = 5The interval where 5 belongs to is 0 < x < 9
[tex]\begin{gathered} \text{function for }0e) f(9): 0 < x < 9 include numbers between 0 and 9 without including 0 and 9the interval 9 will fall on is x ≥ 9
[tex]\begin{gathered} \text{function for x }\ge\text{ 9 is f(x) = }5x\text{ + 3} \\ f(9)\text{ = 5(9) + 3} \\ f(9)\text{ = 45 + 3} \\ f(9)\text{ = 48} \end{gathered}[/tex]