`f(x)=2|x|+x` . Which of the options is the correct value of `f(-2)+f(-4)`?

Options

A. f(-3)
B. f(-1)
C. f(2)
D. f(0)

Answer

To solve the problem, we need to calculate the values of \( f(-2) \) and \( f(-4) \) using the function \( f(x) = 2|x| + x \).

### Step 1: Calculate \( f(-2) \)

1. Substitute \( x = -2 \) into the function:
\[ f(-2) = 2|-2| + (-2) \]
2. Calculate the absolute value:
\[ |-2| = 2 \]
3. Substitute this value back into the equation:
\[ f(-2) = 2 \cdot 2 - 2 \]
4. Perform the multiplication:
\[ = 4 - 2 \]
5. Simplify:
\[ f(-2) = 2 \]

### Step 2: Calculate \( f(-4) \)

1. Substitute \( x = -4 \) into the function:
\[ f(-4) = 2|-4| + (-4) \]
2. Calculate the absolute value:
\[ |-4| = 4 \]
3. Substitute this value back into the equation:
\[ f(-4) = 2 \cdot 4 - 4 \]
4. Perform the multiplication:
\[ = 8 - 4 \]
5. Simplify:
\[ f(-4) = 4 \]

### Step 3: Calculate \( f(-2) + f(-4) \)

1. Now, add the two results:
\[ f(-2) + f(-4) = 2 + 4 \]
2. Simplify:
\[ = 6 \]

### Final Result

The value of \( f(-2) + f(-4) \) is \( 6 \).