\( F(x)=\left\{\begin{array}{ccc}2 x+1 & \text { si } & -1>x \\ -2 & \text { si } & x \geq-1\end{array}\right\} \) en \( x=-1 \)

To solve the problem, we need to evaluate the function \( F(x) \) at \( x = -1 \). The function \( F(x) \) is defined piecewise, which means it has different formulas for different intervals of \( x \). The function is defined as follows: \[ F(x) = \begin{cases} 2x + 1 & \text{if } -1 > x \\ -2 & \text{if } x \geq -1 \end{cases} \] We need to determine which formula to use for \( x = -1 \). Since \( x = -1 \) is equal to -1, it falls into the second interval where \( x \geq -1 \). Therefore, we use the second formula: \[ F(x) = -2 \] Now, we substitute \( x = -1 \) into this formula: \[ F(-1) = -2 \] So, the value of the function \( F(x) \) at \( x = -1 \) is \( -2 \).