It seems like you're asking to evaluate the function $F(x) = e^x + 1$ at $x = \frac{1}{2}$.

To do this, simply substitute $x = \frac{1}{2}$ into the equation:

$F\left(\frac{1}{2}\right) = e^{\frac{1}{2}} + 1$

Now, $e^{\frac{1}{2}}$ is approximately 1.64872. Therefore:

$F\left(\frac{1}{2}\right) = 1.64872 + 1 = 2.64872$

So, the value of $F\left(\frac{1}{2}\right)$ is approximately 2.64872.

Would you like further details on how this was calculated or have any other questions?

Here are 5 related questions:

1. How do you calculate $e^x$ more precisely?
2. What is the derivative of $F(x) = e^x + 1$?
3. How does the value of $F(x)$ change for larger values of $x$?
4. What are the key properties of the exponential function $e^x$?
5. How would you solve an equation involving $F(x) = e^x + 1$?

Tip: Remember that $e^x$ is a transcendental number, meaning it cannot be expressed as a simple fraction or radical.