Use the table to evaluate each expression, if possible.
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Identify the functions ƒ and g from the given table. The table should provide values of ƒ(x) and g(x) for various x, including x = 1.
Locate the value of ƒ(1) in the table by finding the row where x = 1 and noting the corresponding ƒ(x) value.
Locate the value of g(1) in the table by finding the row where x = 1 and noting the corresponding g(x) value.
Add the two values together to find (ƒ + g)(1), using the formula: \[(ƒ + g)(1) = ƒ(1) + g(1)\]
If either ƒ(1) or g(1) is not available in the table, then (ƒ + g)(1) cannot be evaluated.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Function Notation and Evaluation
Function notation, such as f(x), represents the output of a function f for an input x. Evaluating a function at a specific value means substituting that value into the function to find the corresponding output. For example, f(1) means finding the value of f when x = 1.
Operations on functions include addition, subtraction, multiplication, and division of two functions. For (f + g)(x), you add the outputs of f(x) and g(x) for the same input x. This means (f + g)(1) = f(1) + g(1), combining the values from each function at x = 1.
When functions are given in table form, you find the function value by locating the input in the table and reading the corresponding output. To evaluate (f + g)(1), find f(1) and g(1) from the table, then add these values. If either value is missing, the expression cannot be evaluated.