Let's solve each expression step by step, given:

• $f(x) = -3x + x = -2x$
• $g(x) = 5$

Now, let's analyze each expression:

1. $(f + g)(x) = -3x^2 + x + 5$:

   • $(f + g)(x) = f(x) + g(x) = -2x + 5$
   • This is incorrect, since the given expression involves $-3x^2$, but $f(x)$ and $g(x)$ don't have any $x^2$ terms.

2. $(f + g)(x) = -3x^2 + x + 5$:

   • This repeats the previous equation and is still incorrect for the same reason.

3. $(f - g)(x) = 3x^2 + x - 5$:

   • $(f - g)(x) = f(x) - g(x) = -2x - 5$
   • This is incorrect. The expression involves $3x^2$, which does not exist in $f(x)$ or $g(x)$.

4. $(f - g)(x) = -3x^2 - x - 5$:

   • This expression introduces $-3x^2$, which is not present in $f(x)$ or $g(x)$, so it is incorrect.

5. $(fg)(x) = -15x^2 + 5$:

   • $(fg)(x) = f(x) \cdot g(x) = (-2x) \cdot 5 = -10x$
   • This is incorrect because the expression has $-15x^2$, but the correct result should be $-10x$.

6. $(fg)(x) = -15^2 + 5x$:

   • This is incorrect. It seems to misapply the multiplication of $f(x) \cdot g(x)$. The correct result for $fg(x)$ should be $-10x$, not $-15^2 + 5x$.

Conclusion:

None of the expressions provided are correct based on the functions $f(x) = -2x$ and $g(x) = 5$.

Would you like further clarification or a different problem explored?

Related Questions:

1. How do you properly add two functions like $f(x)$ and $g(x)$?
2. How do you subtract functions like $f(x)$ and $g(x)$?
3. What is the proper method to multiply two functions, like $f(x)$ and $g(x)$?
4. How do you handle powers of $x$ when adding or subtracting functions?
5. Can you provide examples of multiplying more complex functions?

Tip:

When multiplying functions, multiply the entire terms, not just the coefficients or parts of the function.