Respuesta :
Composite functions are functions made by composition of two or more functions. The needed function is: Option A: [tex](k\circ p)(x) = 2x^2 -16x + 24[/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]
where the x is the input to first function.
Thus, we have;
[tex](f\circ g)(x) = f(g(x))[/tex]
For the given case, we have [tex]k(x) = 2x^2 - 8[/tex] and [tex]p(x) = x − 4[/tex]
Doing the composition, we get
[tex](k\circ p)(x) = k(p(x)) = 2(p(x))^2 - 8 = 2(x-4)^2 - 8 = 2x^2 + 32 -16x -8\\(k\circ p)(x) = 2x^2 -16x + 24[/tex]
Thus, The needed function is given by Option A: [tex](k\circ p)(x) = 2x^2 -16x + 24[/tex]
Learn more about composite functions (function of functions) here:
https://brainly.com/question/24780056
