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 Composition

Function composition involves combining two functions to create a new function. The notation (ƒ∘g)(x) means to apply g first and then apply f to the result of g. In this case, you first evaluate g(2) and then use that result as the input for f.

Evaluating Functions

Evaluating a function means substituting a specific value into the function's formula. For example, to evaluate g(2) for the function g(x) = x^2, you replace x with 2, resulting in g(2) = 2^2 = 4. This step is crucial for function composition.

Order of Operations

The order of operations is a set of rules that dictates the sequence in which mathematical operations should be performed. In function composition, you must first evaluate the inner function before applying the outer function, ensuring accurate results. This principle is essential for correctly solving expressions involving multiple functions.