To find $f(g(2))$, we first need to compute $g(2)$ and then use that result to find $f(g(2))$.

Step 1: Calculate $g(2)$

Given the function $g(x) = x^2 + x - 1$, substitute $x = 2$:

$g(2) = 2^2 + 2 - 1$

$g(2) = 4 + 2 - 1 = 5$

Step 2: Calculate $f(g(2)) = f(5)$

Now we need to use the result of $g(2) = 5$ in the function $f(x) = -2x + 4$:

$f(5) = -2 \cdot 5 + 4$

$f(5) = -10 + 4 = -6$

Conclusion

$f(g(2)) = -6$

Would you like more details or have any questions?

Here are 5 related questions for further practice:

1. What is $g(f(2))$ for the same functions?
2. Find $f(g(x))$ in terms of $x$.
3. Calculate the value of $g(g(1))$.
4. If $h(x) = x^3 - 2x$, what is $f(h(1))$?
5. Determine the roots of the equation $f(x) = 0$.

Tip: When solving composite functions, always start from the innermost function and work outward.