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 a clear and concise manner. In this case, ƒ(x) and g(x) denote two different functions, where ƒ(x) = x + 1 and g(x) = x². Understanding how to interpret and manipulate these notations is essential for evaluating expressions involving functions.

Composition of Functions

The composition of functions involves combining two functions to create a new function. The notation (ƒ/g)(x) represents the division of the function ƒ by the function g. To evaluate (ƒ/g)(2), one must first compute ƒ(2) and g(2), and then divide the results, illustrating the relationship between the two functions.

Evaluating Functions

Evaluating functions means substituting a specific value into the function's expression to find the output. For example, to evaluate ƒ(2) and g(2), you replace x with 2 in their respective formulas. This step is crucial for calculating (ƒ/g)(2), as it requires the outputs of both functions at x = 2 to perform the division.