Questions: For the given functions f and g, complete parts (a)-(h). For parts (a)-(d), also find the domain. f(x)=x-8 ; g(x)=2x^2 What is the domain of f-g? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The domain is x . (Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. The domain is x x is any real number .

Solution Steps

To find the domain of $f - g$, we need to determine the set of all $x$ values for which both $f(x)$ and $g(x)$ are defined. Since $f(x) = x - 8$ and $g(x) = 2x^2$ are both polynomials, they are defined for all real numbers. Therefore, the domain of $f - g$ is all real numbers.

The domain of $f - g$ is all real numbers because both $f(x)$ and $g(x)$ are defined for all real numbers.

We have the functions defined as follows: $$f(x) = x - 8$$ $$g(x) = 2x^2$$

Both $f(x)$ and $g(x)$ are polynomial functions. Polynomial functions are defined for all real numbers. Therefore, the domain of each function is: $$\text{Domain of } f: \{ x \mid x \in \mathbb{R} \}$$ $$\text{Domain of } g: \{ x \mid x \in \mathbb{R} \}$$

To find the domain of $f - g$, we need to consider the intersection of the domains of $f$ and $g$. Since both functions are defined for all real numbers, the domain of $f - g$ is also: $$\text{Domain of } (f - g): \{ x \mid x \in \mathbb{R} \}$$

Final Answer