1 Answer

Seoman · Answer 1 · 2023-11-05T18:52:06+0000

Given

$\begin{gathered} f(x)\text{ =5x -2 , x <}1 \\ f(x)=\text{ -x + 8 , x }\ge\text{ 1} \end{gathered}$

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

$f(x)\text{ = 5x - 2}$

Substituting the value of x into f(x):

$\begin{gathered} f(-2)=\text{ 5\lparen-2\rparen}-\text{ 2} \\ =\text{ -10 - 2} \\ =\text{ -12} \end{gathered}$

At x = 3

$f(x)=\text{ -x + 8}$

Substituting the value of x into f(x):

$\begin{gathered} f(3)\text{= -3 + 8} \\ =\text{ 5} \end{gathered}$

Next, we sum f(-2) and f(3):

$\begin{gathered} f(-2)\text{ + f\lparen3\rparen = -12 + 5} \\ =\text{ -7} \end{gathered}$

Answer: -7 (Option B)

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