Given functions f and g, find (b)(g∘ƒ)(x) and its domain. See Examples 6 and 7. ƒ(x)=√x, g(x)=x+3

Key Concepts

Function Composition

Function composition involves combining two functions, where the output of one function becomes the input of another. In this case, (g∘ƒ)(x) means applying the function f first and then applying g to the result. Understanding how to correctly perform this operation is essential 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 composition of functions, the domain is determined by the restrictions of both functions involved. In this case, we need to consider the domain of f(x) = √x and how it affects the overall composition with g.

Square Root Function

The square root function, denoted as f(x) = √x, is defined only for non-negative values of x, meaning x must be greater than or equal to zero. This restriction is crucial when determining the domain of the composed function (g∘ƒ)(x), as it influences the valid inputs for the entire expression.