To find $f(g(x))$, we substitute $g(x)$ into the function $f(x)$.

Given:

• $f(x) = x - 2$
• $g(x) = \sin(x) + \tan(x)$

We substitute $g(x)$ into $f(x)$:

$f(g(x)) = f(\sin(x) + \tan(x))$

Now, using the definition of $f(x)$, replace $x$ with $\sin(x) + \tan(x)$:

$f(g(x)) = (\sin(x) + \tan(x)) - 2$

So, the composition function is:

$f(g(x)) = \sin(x) + \tan(x) - 2$

Let me know if you'd like further details or if you have any questions.

Here are 5 related questions:

1. What is the domain of $f(g(x))$?
2. How would you find $g(f(x))$ using the given functions?
3. How do the trigonometric properties of $\sin(x)$ and $\tan(x)$ affect the behavior of $f(g(x))$?
4. What happens if we differentiate $f(g(x))$?
5. What are the zeros of $f(g(x))$?

Tip: Always check the domains of composite functions to ensure they are well-defined.