
Select all that apply. Given f(x) =-3x+x and g(x) = 5.
(f+g)(x) = -3x^2+x+5
(f+g)(x)-3x^2+x+5
(f-g)(x)=3x^2+x-5
(f-g)(x)-3x^2-x-5
(fg)(x)=-15x^2+5
(fg)(x)=-15^2+5x

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.

Select all that apply. Given f(x) = -3x + x and g(x) = 5. (f+g)(x) = -3x^2 + x + 5 (f+g)(x) -3x^2 + x + 5 (f-g)(x) = 3x^2 + x - 5 (f-g)(x) -3x^2 - x - 5 (fg)(x) = -15x^2 + 5 (fg)(x) = -15^2 + 5x

Explore how to perform basic operations like addition, subtraction, and multiplication on functions. This problem covers essential algebraic concepts, including how to add, subtract, and multiply f(x) = -2x and g(x) = 5. Suitable for students in Grades 9-10.

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