Question

Find the rule for (Æ’ ° g)(x) and (g ° f)(x) and give the domain of each composite function.

Answer 1

To find the rule for (Æ’ ° g)(x) and (g ° Æ’)(x), substitute x into Æ’(x) and g(x) in the appropriate order to find the composite functions.

Step-by-step explanation:

To find the rule for (Æ’ ° g)(x) and (g ° f)(x), we need to know the functions Æ’(x) and g(x). Once we have that information, we can substitute x into Æ’(x) and g(x) in the appropriate order to find the composite functions.

For (Æ’ ° g)(x), we first substitute x into g(x) to find g(x) = g(x).

Then we substitute g(x) into Æ’(x) to find Æ’(g(x)). This is the composite function (Æ’ ° g)(x).

For (g ° Æ’)(x), we first substitute x into Æ’(x) to find Æ’(x) = Æ’(x).

Then we substitute Æ’(x) into g(x) to find g(Æ’(x)). This is the composite function (g ° Æ’)(x).

The domain of each composite function depends on the domain of Æ’(x) and g(x). If the domains of Æ’(x) and g(x) intersect, that intersection becomes the domain of the composite function.