Question

What is the value of f(-2) + f(3)?0-170 – 7O 10O 23

Answer 1

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)