Here are the essential concepts you must grasp in order to answer the question correctly.
Function Composition
Function composition involves combining two functions, where the output of one function becomes the input of another. In this case, (f o g)(x) means applying g first and then applying f to the result of g. Understanding how to correctly substitute and evaluate these functions is crucial for solving the problem.
Recommended video:
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 of f o g is determined by the domain of g and the values that g outputs that are also valid inputs for f. This requires analyzing both functions to ensure all inputs are permissible.
Recommended video:
Domain Restrictions of Composed Functions
Square Root Function
The square root function, f(x) = √x, is defined only for non-negative values of x, meaning x must be greater than or equal to zero. This restriction impacts the overall domain of the composed function f o g, as any output from g(x) that is negative will not be valid for f. Understanding this restriction is essential for determining the domain of the composition.
Recommended video:
Imaginary Roots with the Square Root Property