Respuesta :
Composite functions are functions of functions. The needed composite function for given context is: [tex]P(J(y)) = \dfrac{2}{3}J(y) - 2[/tex]
What are function of functions and how are they represented?
Function of function, as the name suggests, are functions applied over functions themselves. This is also called function composition.
We have input. We apply one function on that input. Then we apply another function on the output obtained by the first function. This whole function application on first input is called function of functions. The resultant function which maps the input x to the final output is called function of function.
If first function is g( and the other function is f, then we can write the resultant function of function as [tex](f\circ g)(x)[/tex]input to first function.
Thus, we have;
[tex](f\circ g)(x) = f(g(x))[/tex]
For the given case, it is given that:
- [tex]P(w) = \dfrac{2}{3}w - 2[/tex]
- [tex]J(y)[/tex]
To evaluate how many paintings Jojo completes in a year, we need [tex]P(J(y))[/tex] (since, we need number of paintings and input is year, so we convert year to number of weeks by function J, and then give the output to P function to evaluate number of paintings)
Thus,
[tex]P(w) = \dfrac{2}{3}w - 2\\\\P(J(y)) = \dfrac{2}{3}J(y) - 2[/tex]
Thus,
The needed composite function for given context is: [tex]P(J(y)) = \dfrac{2}{3}J(y) - 2[/tex]
Learn more about composite functions here:
https://brainly.com/question/24780056
