High School

What is the domain of the function \( f + g \)?

A. \( f(x) = 4x^2 + 34x + 42, \quad g(x) = x + 7 \)

B. \( f(x) = 4x^2 + 34x + 42 + g(x) \)

C. \( f(x) = 4x^2 + 34x + 42 - g(x) \)

D. \( f(x) = 4x^2 + 34x + 42 \times g(x) \)

Answer :

Final answer:

The functions f(x) = x² and g(s) = s² are essentially the same because they perform the same operation on their input, despite using different variable names (x and s).

Explanation:

The question asked is whether the functions f and g are the same or different, given that f(x) = x² and g(s) = s². These functions are essentially the same in their operational structure, meaning they both square their input. However, the difference lies in the notation of the independent variable: x for f and s for g. This does not change the mathematical behavior or the outcome of the functions, making their functional forms identical when considering the operation performed on their inputs.

Thus, f and g are the same function in terms of how they operate (both square their respective input), but they are presented with different variable notations.