Question

Question was provided via image upload.

Explanation:

Identify the missing information

The provided image is extremely blurry and cropped, showing only the lower parts of a math problem regarding function operations:

1. Finding \((f+g)(x)\) and the domain of \(f+g\).
2. Finding \((f-g)(x)\) and the domain of \(f-g\).

Crucially, the definitions of the functions \(f(x)\) and \(g(x)\) are completely cut off and missing from the top of the image. Without knowing the formulas for \(f(x)\) and \(g(x)\), it is mathematically impossible to compute the specific algebraic expressions for \((f+g)(x)\) and \((f-g)(x)\) or determine their exact domains.

Explain the general concepts

To help you solve this once you have the full image, let's review how these operations work using the relevant concepts:

Using the Function Operations knowledge point:

• The sum function is defined as:

$$ (f+g)(x) = f(x) + g(x) $$

• The difference function is defined as:

$$ (f-g)(x) = f(x) - g(x) $$

Using the Interval Notation knowledge point:

• The domain of both \((f+g)(x)\) and \((f-g)(x)\) is the intersection of the domain of \(f(x)\) and the domain of \(g(x)\):

$$ \text{Domain}(f \pm g) = \text{Domain}(f) \cap \text{Domain}(g) $$

• For example, if both \(f(x)\) and \(g(x)\) are polynomials, their domains are all real numbers, written in interval notation as \((-\infty, \infty)\).

Answer:

The definitions for the functions \(f(x)\) and \(g(x)\) are cut off at the top of the image, making it impossible to calculate the exact simplified expressions or domains.

Please upload a complete, clear image showing the formulas for \(f(x)\) and \(g(x)\) so we can solve it step-by-step!