*f*(*x*) = *x*2 + 7,    *g*(*x*) = 

6 − *x*

(a)    (*f* + *g*)(*x*) =

Given the functions \( f(x) = x^2 + 7 \) and \( g(x) = 6 - x \), you are asked to find \( (f + g)(x) \), which represents the sum of the two functions.

### Step-by-step solution:

1. \( f(x) = x^2 + 7 \)
2. \( g(x) = 6 - x \)
3. To find \( (f + g)(x) \), you add the two functions:
   \[
   (f + g)(x) = f(x) + g(x) = (x^2 + 7) + (6 - x)
   \]

4. Combine like terms:
   \[
   (f + g)(x) = x^2 - x + 7 + 6 = x^2 - x + 13
   \]

### Final Answer:
\[
(f + g)(x) = x^2 - x + 13
\]

Would you like further details on this, or do you have any questions?

Here are 5 related questions for further practice:

1. What is \( (f - g)(x) \) for the same functions?
2. Find \( (f \cdot g)(x) \) for these functions.
3. What is the value of \( (f + g)(2) \)?
4. Determine the domain of \( f(x) \) and \( g(x) \).
5. If \( f(x) = g(x) \), what is the solution for \( x \)?

**Tip:** When adding or subtracting functions, always combine like terms carefully to simplify the result.

f(x) = x^2 + 7, g(x) = 6 − x. (a) (f + g)(x) =

Learn how to add two functions, f(x) = x^2 + 7 and g(x) = 6 − x, to find (f + g)(x). This problem involves polynomial functions, combining like terms, and understanding basic function operations. Suitable for students in Grades 9-10.

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