find f of g given that f(x)=x-2 and g(x)=sin(x)+tan(x)

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.

This page explains how to solve the composition of functions problem where f(x) = x - 2 and g(x) = sin(x) + tan(x). Learn how to substitute g(x) into f(x) and get the resulting function. Suitable for students in Grades 10-12 studying trigonometry and functions.

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