$(f-g)(x) =$
A. $x^2+x-4$
B. $x^2+x+4$
C. $4^2-x+6$
D. $x^2+x+6$
Answer (2)
Without knowing the expressions for f ( x ) and g ( x ) , it is impossible to determine ( f − g ) ( x ) . The question is incomplete and cannot be answered without additional information.
Explanation
Problem Analysis The question asks us to find the expression for ( f − g ) ( x ) , given a list of possible answers. However, we are not given the expressions for the functions f ( x ) and g ( x ) . Without knowing f ( x ) and g ( x ) , we cannot determine ( f − g ) ( x ) . Therefore, we need to make an assumption or look for a pattern in the given options.
Analyzing the Options Let's analyze the given options:
Option 1: x 2 + x − 4 Option 2: x 2 + x + 4 Option 3: 4 2 − x + 6 = 16 − x + 6 = 22 − x Option 4: x 2 + x + 6
Since we don't have any information about f ( x ) and g ( x ) , we cannot definitively choose one of these options. However, if we assume that the question intends for us to pick the 'most reasonable' answer, we might look for an option that is a polynomial, as polynomial functions are common. Options 1, 2, and 4 are quadratic polynomials, while option 3 is a linear polynomial. Without further information, it's impossible to determine the correct answer.
Conclusion Since we cannot determine the correct answer without knowing f ( x ) and g ( x ) , we must assume that there is some missing information or context. If we assume that the question is asking which of the options could be ( f − g ) ( x ) for some functions f ( x ) and g ( x ) , then any of the options are possible. However, without any additional information, we cannot definitively choose one.
Examples
In calculus, when analyzing the difference between two functions, such as profit and cost functions, the expression (f-g)(x) represents the net outcome. For example, if f(x) represents the revenue from selling x items and g(x) represents the cost of producing x items, then (f-g)(x) represents the profit. Understanding how to find and interpret (f-g)(x) is crucial for making informed business decisions.
The expression ( f − g ) ( x ) cannot be determined without knowing the specific functions f ( x ) and g ( x ) . All provided answer options require more context to choose the correct one. Thus, it's impossible to select an option based solely on the given information.
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