To find $(f+g)(x)$, we need to add the functions $f(x)$ and $g(x)$ together:

$f(x) = 15 - 2x - x^2$ $g(x) = 2x^2 + 10x - 1$

Now, we calculate:

$(f+g)(x) = f(x) + g(x) = (15 - 2x - x^2) + (2x^2 + 10x - 1)$

Combine like terms:

• Constant terms: $15 - 1 = 14$
• $x$ terms: $-2x + 10x = 8x$
• $x^2$ terms: $-x^2 + 2x^2 = x^2$

Therefore,

$(f+g)(x) = x^2 + 8x + 14$

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

1. How do you find $(f-g)(x)$ using the same functions?
2. What is the vertex of the parabola represented by $(f+g)(x)$?
3. How would you find the roots of $(f+g)(x)$?
4. Can you determine the domain and range of $(f+g)(x)$?
5. How does the graph of $(f+g)(x)$ compare to the graphs of $f(x)$ and $g(x)$ individually?

Tip: When combining functions, always group and simplify like terms carefully to avoid mistakes!