How do you find the domain of a composite function?

Find the domain of f. Find those inputs, x, in the domain of g for which g(x) is in the domain of f. That is, exclude those inputs, x, from the domain of g for which g(x) is not in the domain of f. The resulting set is the domain of f ∘ g \displaystyle f\circ g f∘g.

How do you find the domain and range of a composite function?

What is the domain and Codomain of a composite function?

then the codomain of fn∘fn−1∘⋯∘f1 is An+1, which is the codomain of fn. Likewise, the domain of a composite is always the domain of the first function in the composite (i.e. the last appearing in the string), so the domain of fn∘⋯∘f1 is A1, which is the domain of f1. You can apply this general result to your problem.

What is the range of a composite function?

The range of a function is the set of all values a function can take. For example, the range of the function f(x) = ex is given by f(x) > 0, because ex is always greater than zero. As another example, if f(x) = sin x then the range is given by −1 ≤ f(x) ≤ 1.

How do you find the domain?

Let y = f(x) be a function with an independent variable x and a dependent variable y. If a function f provides a way to successfully produce a single value y using for that purpose a value for x then that chosen x-value is said to belong to the domain of f.