Use the table to evaluate each expression, if possible.
$open paren f of slash g close paren times 0$

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Identify the functions $ f(x) $ and $ g(x) $ from the given table. You need to find the values of $ f(0) $ and $ g(0) $ by looking up the corresponding outputs when $ x = 0 $.

Recall that the expression $ (f/g)(0) $ means $ \frac{f(0)}{g(0)} $. This is the value of the function $ f(x) $ divided by the value of the function $ g(x) $ at $ x = 0 $.

Check if $ g(0) $ is not zero because division by zero is undefined. If $ g(0) = 0 $, then $ (f/g)(0) $ is undefined and cannot be evaluated.

If $ g(0) \neq 0 $, substitute the values of $ f(0) $ and $ g(0) $ into the fraction $ \frac{f(0)}{g(0)} $.

Simplify the fraction if possible to express the final value of $ (f/g)(0) $.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Function Notation and Evaluation

Function notation, such as f(x) or g(x), represents the output of a function for a given input x. Evaluating a function at a specific value means substituting that value into the function's formula or table to find the corresponding output.

Function Division (Quotient of Functions)

The quotient of two functions (f/g)(x) is defined as f(x) divided by g(x), provided g(x) ≠ 0. This operation combines two functions by dividing their outputs for the same input, and it is important to check the denominator to avoid division by zero.

Using Tables to Evaluate Functions

When functions are given in table form, values of f(x) and g(x) at specific inputs are listed. To evaluate expressions like (f/g)(0), locate the values of f(0) and g(0) in the table and perform the required operation, ensuring the denominator is not zero.

Use the table to evaluate each expression, if possible. (f/g)(0)(f/g) (0)