F(x)=x−4/2-3x Find the range of the function and state the condition in a set notation form

The function is given as $F(x)=x-4/2-3x$. According to the order of operations, division is performed before subtraction.

Combine the terms involving $x$:

The simplified function $F(x) = -2x - 2$ is a linear function of the form $y = mx + c$, where $m = -2$ (the slope) and $c = -2$ (the y-intercept).

For any linear function $y = mx + c$ where the slope $m \neq 0$, the function can take any real value. In this case, $m = -2$, which is not zero. Therefore, as $x$ varies over all real numbers, $F(x)$ will also vary over all real numbers.

The range of the function is all real numbers.

The final answer is $\{y \mid y \in \mathbb{R}\}$.