Given
[tex]\begin{gathered} f(x)\text{ =5x -2 , x <}1 \\ f(x)=\text{ -x + 8 , x }\ge\text{ 1} \end{gathered}[/tex]
Required: f(-2) + f(3)
The given function f(x) is a piece-wise function . This implies that the function is defined differently at different range of x
For the given problem
At x = -2
[tex]f(x)\text{ = 5x - 2}[/tex]
Substituting the value of x into f(x):
[tex]\begin{gathered} f(-2)=\text{ 5\lparen-2\rparen}-\text{ 2} \\ =\text{ -10 - 2} \\ =\text{ -12} \end{gathered}[/tex]
At x = 3
[tex]f(x)=\text{ -x + 8}[/tex]
Substituting the value of x into f(x):
[tex]\begin{gathered} f(3)\text{= -3 + 8} \\ =\text{ 5} \end{gathered}[/tex]
Next, we sum f(-2) and f(3):
[tex]\begin{gathered} f(-2)\text{ + f\lparen3\rparen = -12 + 5} \\ =\text{ -7} \end{gathered}[/tex]
Answer: -7 (Option B)
