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

Key Concepts

Function Division

Function division involves creating a new function by dividing one function by another. In this case, (f/g)(x) is defined as f(x) divided by g(x), which requires both functions to be defined at the same x-value. Understanding how to perform this operation is crucial for finding the resulting 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, the domain must consider restrictions such as square roots (which require non-negative inputs) and denominators (which cannot be zero). Identifying the domain is essential for ensuring the function behaves correctly.

Square Root Function

A square root function, like f(x) = √(4x - 1), is defined only for values of x that make the expression under the square root non-negative. This means that 4x - 1 must be greater than or equal to zero, leading to a specific range of x-values. Understanding this concept is vital for determining the domain of f(x).