Question

For the pair of functions f and g, determine the domain of the sum, difference and product of the two functions. f(x) = x - 10 - 9(x) = 10x³ g(x) = x² What is the domain of the sum of f and g? (A) (x | x is a real number and x² ≥ 0) (B) (x | x is a real number and x² > 0) (C) (x | x is a real number and x² ≤ 0) (D) (x | x is a real number) What is the domain of the difference of f and g? (A) (x | x is a real number and x² ≥ 0) (B) (x | x is a real number and x² > 0) (C) (x | x is a real number and x² ≤ 0) (D) (x | x is a real number) What is the domain of the product of f and g? (A) (x | x is a real number and x² ≥ 0) (B) (x | x is a real number and x² > 0) (C) (x | x is a real number and x² ≤ 0) (D) (x | x is a real number)

Answer 1

The domain of functions f(x) and g(x), as well as their sum, difference, and product, is all real numbers.

Step-by-step explanation:

The domain of these functions, f(x) and g(x), refers to the set of all possible input values (x-values) which will output real numbers.

In this case, both f(x) = x - 10 - 9(x) = 10x³ and g(x) = x² are defined for all real numbers since there are no restrictions or limitations on x. Consequently, the sum, difference and product of these two functions are also defined for all real numbers.

Therefore, the domain of the sum of f and g is (D) (x | x is a real number). Similarly, the domain of the difference of f and g is also (D) (x | x is a real number). Lastly, the domain of the product of f and g is also (D) (x | x is a real number).

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