lanedance said:start with finding the domain of g(x) and f(x)
A composite function is a function that is created by combining two or more functions. The output of one function is used as the input for another function, creating a new function.
To find the domain of a composite function, you need to first find the domain of each individual function in the composite. Then, you need to determine which inputs will satisfy all of the individual function's domains. These inputs will be the domain of the composite function.
Yes, the domain of a composite function can be different from the domain of its individual functions. This is because when combining functions, certain inputs may be restricted due to the combination of the individual functions' domains.
Some common mistakes when finding the domain of a composite function include forgetting to consider all of the individual functions' domains, not accounting for restrictions that may occur when combining functions, and not simplifying the final domain expression.
Yes, a composite function can have an empty domain if the combination of the individual functions' domains results in no valid inputs. This can occur if there are restrictions or contradictions when combining the individual functions.