Questions: Given the function below, evaluate f(0) f(x) = 5 - 4-5x + 2

Solution Steps

To evaluate \( f(0) \) for the given function \( f(x) = 5 - 4|-5x + 2| \), we need to substitute \( x = 0 \) into the function and simplify the expression.

1. Substitute \( x = 0 \) into the function \( f(x) \).
2. Simplify the expression inside the absolute value.
3. Calculate the absolute value.
4. Multiply by -4 and add 5 to get the final result.

We start by substituting \( x = 0 \) into the function \( f(x) \): \[ f(0) = 5 - 4|-5(0) + 2| \]

Next, we simplify the expression inside the absolute value: \[ f(0) = 5 - 4|-0 + 2| = 5 - 4|2| \]

Now, we calculate the absolute value: \[ |2| = 2 \] Thus, we have: \[ f(0) = 5 - 4 \cdot 2 \]

Now we perform the multiplication: \[ f(0) = 5 - 8 \] Finally, we calculate: \[ f(0) = -3 \]

Final Answer