perform the fundamental operation  with solution$$  $$ of $$ f\left(x\right)=x^2 $$$$ +g\left(x\right)=x-3 $$

To perform the fundamental operation with the functions $ f(x) = x^2 $ and $ g(x) = x - 3 $, we generally consider the sum of these functions, denoted as $ (f + g)(x) $.

### Operation:
\[
(f + g)(x) = f(x) + g(x)
\]

### Substituting the given functions:
\[
(f + g)(x) = x^2 + (x - 3)
\]

### Simplifying:
\[
(f + g)(x) = x^2 + x - 3
\]

### Final Answer:
\[
(f + g)(x) = x^2 + x - 3
\]

This is the expression for the sum of the functions $ f(x) $ and $ g(x) $.

Would you like more details or have any questions? Here are some related questions:

1. How do you perform subtraction of two functions?
2. What happens when you multiply $ f(x) $ and $ g(x) $?
3. How do you find the composition $ f(g(x)) $ with these functions?
4. Can you find the derivative of $ (f + g)(x) $?
5. What is the domain of the function $ (f + g)(x) $?

**Tip:** When performing operations with functions, always pay attention to combining like terms.

Learn how to perform fundamental operations with functions f(x) = x^2 and g(x) = x - 3 by calculating their sum. This problem covers basic concepts in function operations, including addition of functions and simplification of algebraic expressions. Suitable for Grades 9-12.

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