Let ƒ(x) = √(x-2) and g(x) = x^2. Find each of the following, if possible. (ƒ ○ g)(x)

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 ƒ to the result of g. This process requires substituting g(x) into ƒ, resulting in ƒ(g(x)). Understanding this concept is crucial for solving the problem.

Domain of a Function

The domain of a function is the set of all possible input values (x-values) for which the function is defined. For the function ƒ(x) = √(x-2), the expression under the square root must be non-negative, meaning x must be greater than or equal to 2. Identifying the domain is essential to ensure that the composed function is valid.

Quadratic Functions

Quadratic functions are polynomial functions of degree two, typically expressed in the form g(x) = x^2. They have a parabolic graph and can take any real number as input. Understanding the behavior of quadratic functions is important when determining the output of g(x) and how it interacts with the function ƒ in the composition.