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

Key Concepts

Function Composition

Function composition involves combining two functions, where the output of one function becomes the input of another. In this case, the composition ƒ ○ g means we will evaluate ƒ at g(x), or ƒ(g(x)). Understanding how to properly substitute one function into another 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, which imposes restrictions on the values of x. Identifying the domain is essential to ensure that the composed function is valid.

Composite Function Domain

When finding the domain of a composite function like ƒ ○ g, we must consider the domains of both functions involved. Specifically, we need to ensure that g(x) falls within the domain of ƒ. This means we must first determine the domain of g(x) and then check which outputs of g(x) are valid inputs for ƒ(x).