To find $f(g(x))$, we first need to evaluate $g(x)$ and then substitute that result into $f(x)$.

1. Find $g(x)$: $g(x) = x + 1$

2. Substitute $g(x)$ into $f(x)$: $f(g(x)) = f(x + 1)$

3. Evaluate $f(x + 1)$: $f(x) = x^2 - 2x$ Substitute $x + 1$ into $f(x)$: $f(x + 1) = (x + 1)^2 - 2(x + 1)$

4. Simplify: $= (x^2 + 2x + 1) - (2x + 2)$ $= x^2 + 2x + 1 - 2x - 2$ $= x^2 - 1$

Thus, $f(g(x)) = x^2 - 1$.

If you need any further details or have questions, let me know! Here are some follow-up questions you might consider:

1. What is $g(f(x))$?
2. How would you graph $f(x)$ and $g(x)$?
3. Can you find the roots of $f(g(x))$?
4. How would you find the derivative of $f(g(x))$?
5. What would happen if $g(x)$ was defined differently?

Tip: Always remember to substitute carefully when working with composite functions!