A function F is defined as follow :
for `x gt 0, F(x) = x^6- x^3- 17x - 17`
for `x lt 0, F(x) = -x^6-x^2+17x-17`
What is the value of F (-1) ?

Options

A. `-36`
B. `-2`
C. 0
D. 2

Answer

To find the value of \( F(-1) \) for the given piecewise function, we will follow these steps:

1. **Identify the appropriate function definition**: Since we are looking for \( F(-1) \) and \(-1 < 0\), we will use the function defined for \( x < 0 \):
\[ F(x) = -x^6 - x^2 + 17x - 17 \]

2. **Substitute \( x = -1 \) into the function**:
\[ F(-1) = -(-1)^6 - (-1)^2 + 17(-1) - 17 \]

3. **Calculate each term**:
- Calculate \((-1)^6\):
\[ (-1)^6 = 1 \]
- Calculate \((-1)^2\):
\[ (-1)^2 = 1 \]
- Now substitute these values back into the equation:
\[ F(-1) = -1 - 1 - 17 - 17 \]

4. **Combine the terms**:
\[ F(-1) = -1 - 1 - 17 - 17 = -2 - 34 = -36 \]

Thus, the value of \( F(-1) \) is:
\[ \boxed{-36} \]