Problem

Given the function \[ f(x)=\left\{\begin{array}{ll} 2 x+2 & x<0 \\ 2 x+4 & x \geq 0 \end{array}\right. \] Calculate the following values: \[ \begin{array}{l} f(-1)= \\ f(0)= \\ f(2)= \end{array} \]

Solution

Step 1 :The given function is defined as \(f(x)=\left\{\begin{array}{ll} 2x+2 & x<0 \\ 2x+4 & x \geq 0 \end{array}\right.\)

Step 2 :We need to calculate the values of \(f(-1)\), \(f(0)\), and \(f(2)\).

Step 3 :For \(f(-1)\), since -1 is less than 0, we use the formula \(2x + 2\).

Step 4 :For \(f(0)\), since 0 is not less than 0, we use the formula \(2x + 4\).

Step 5 :For \(f(2)\), since 2 is not less than 0, we use the formula \(2x + 4\).

Step 6 :Calculating these values, we find that \(f(-1) = 2*(-1) + 2 = 0\), \(f(0) = 2*0 + 4 = 4\), and \(f(2) = 2*2 + 4 = 8\).

Step 7 :So, the final answers are \(f(-1)= \boxed{0}\), \(f(0)= \boxed{4}\), and \(f(2)= \boxed{8}\).

From Solvely APP
Source: https://solvelyapp.com/problems/15944/

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