For the pair of functions defined, find (ƒg)(x). Give the domain of each. See Example 2. ƒ(x)=√(4x-1), g(x)=1/x

Key Concepts

Function Composition

Function composition involves combining two functions, where the output of one function becomes the input of another. In this case, (ƒg)(x) means we will substitute g(x) into ƒ(x). Understanding how to perform this substitution is crucial for finding the composed function.

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 functions given, we need to determine the restrictions on x that would make the functions valid, such as avoiding division by zero or ensuring the expression under a square root is non-negative.

Square Root Function

The square root function, denoted as √(x), is defined only for non-negative values of x. In the function ƒ(x)=√(4x-1), the expression inside the square root must be greater than or equal to zero, which imposes additional constraints on the domain that must be considered when finding (ƒg)(x).