Question

What does $F\left(x\right)$ stand for?

Answer 1

Meaning of $F\left(x\right)$:

$F\left(x\right)$ represents a function.
For all values of $x$, we need to get a unique value of $F\left(x\right)$ then we can say that is a function.

Let us take an example
Let there have two curves
one is an equation of a circle $x^2+y^2=4$ and another one is a straight line $x=1$

The graph is

Here, for the value of $x=1$, we get more than one value of $F\left(x\right)$.

Therefore, it is not a function.

Now, we take two straight line $x=y$ and $x=1$

we get the graph

Here, for the value of $x=1$, we get a single value of $F\left(x\right)$.

Therefore, it is a function.