Questions: What is the value of f(-1) in the piecewise function f(x)= -3x+1 when x>1 -2x when x=1 2x-1 when x<1

Transcript text: What is the value of $f(-1)$ in the piecewise function $f(x)=\{$ \[ \begin{aligned} -3 x+1 & \text { when } \mathrm{x}>1 \\ -2 x & \text { when } \mathrm{x}=1 \\ 2 x-1 & \text { when } \mathrm{x}<1 \end{aligned} \]

Solution

Solution Steps

To find the value of $ f(-1) $ in the given piecewise function, we need to determine which condition $ x = -1 $ satisfies. Since $ -1 < 1 $, we use the expression $ 2x - 1 $.

Step 1: Identify the Appropriate Piecewise Condition

To find the value of $ f(-1) $ in the piecewise function, we need to determine which condition $ x = -1 $ satisfies. The piecewise function is defined as: \[ f(x) = \begin{cases} -3x + 1 & \text{when } x > 1 \\ -2x & \text{when } x = 1 \\ 2x - 1 & \text{when } x < 1 \end{cases} \] Since $ -1 < 1 $, we use the expression $ 2x - 1 $.

Step 2: Substitute $ x = -1 $ into the Appropriate Expression

Substitute $ x = -1 $ into the expression $ 2x - 1 $: \[ f(-1) = 2(-1) - 1 \]

Step 3: Simplify the Expression

Simplify the expression: \[ f(-1) = -2 - 1 = -3 \]