Without using paper and pencil, evaluate each expression given the following functions. ƒ(x)=x+1 and g(x)=x^2 (ƒ+g)(2)

Key Concepts

Function Notation

Function notation is a way to represent mathematical functions. In this case, ƒ(x) and g(x) denote two different functions, where ƒ(x) = x + 1 and g(x) = x². Understanding how to read and interpret these notations is crucial for evaluating expressions involving these functions.

Function Addition

Function addition involves combining two functions to create a new function. The expression (ƒ + g)(x) means to add the outputs of ƒ and g for a given input x. For example, (ƒ + g)(x) = ƒ(x) + g(x), which allows us to evaluate the combined function at specific values.

Evaluating Functions

Evaluating functions means substituting a specific value into the function to find the output. In this question, we need to evaluate (ƒ + g)(2) by first calculating ƒ(2) and g(2), then adding those results together. This process is essential for finding the value of the combined function at the given input.