The function written in the image is:

$g(x) = \arcsin\left(3^{2x} - 3^x + 1 \right) + |x| + \log_{1/4}\left(6\ln(\arccos(x) - \pi)\right) \cdot 6 \cdot \frac{1}{\sqrt{2 - \cosh(x)}} + e^{\sin(x)}$

This function includes various mathematical operations like logarithms, exponentials, trigonometric functions (sine, cosine, hyperbolic cosine), absolute values, and logarithms with non-standard bases. Each part requires careful handling in calculus or algebraic analysis.

Would you like details on any specific part of this function or need help with a calculation related to it?

Here are five related questions to expand on this:

1. How do you differentiate this function $g(x)$?
2. What is the domain of $g(x)$, considering the trigonometric and logarithmic functions?
3. How would you simplify the expression involving $\log_{1/4}(6 \ln(\arccos(x) - \pi))$?
4. What happens when you try to evaluate $g(x)$ at certain values of $x$, such as $x = 0$?
5. Can you integrate this function over a certain interval?

Tip: When dealing with complex expressions, breaking them into smaller parts makes it easier to differentiate or simplify them effectively.