Use the table to evaluate each expression, if possible.
$(\text{ƒ}+g)\left(1\right)$

Verified step by step guidance

1. 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.
2. Locate the value of ƒ(1) in the table by finding the row where x = 1 and noting the corresponding ƒ(x) value.
3. Locate the value of g(1) in the table by finding the row where x = 1 and noting the corresponding g(x) value.
4. Add the two values together to find (ƒ + g)(1), using the formula: \[(ƒ + g)(1) = ƒ(1) + g(1)\]
5. If either ƒ(1) or g(1) is not available in the table, then (ƒ + g)(1) cannot be evaluated.

Key Concepts

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

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.

Using Tables to Evaluate Functions

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.