Answer:
k [p(x)] = 5x -28 .
Option (b) is correct .
Step-by-step explanation:
As given the expression in the questions are
k(x) = 5x - 8
p(x) = x - 4
k [p(x)] = k (x-4)
= 5 × (x-4) -8
= 5× x - 5 × 4 - 8
= 5x - 20 - 8
= 5x - 28
Thus
k [p(x)] = 5x -28
Therefore k [p(x)] = 5x -28 .
Option (b) is correct .
Composite functions are function of functions. The correct value of k[p(x)] for given context is given by: Option b. k[p(x)] = 5x − 28
Function of functions, 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 given context, the functions are:
[tex]k(x) = 5x - 8 \\p(x) = x - 4,[/tex]
Composing them to get k[p(x)], we need to put whatever p(x) output as input to k(x).
Thus,
[tex]k(p(x)) = 5(p(x)) - 8\\\\k(p(x)) = 5(x-4) - 8 = 5x - 20 - 8 = 5x - 28\\[/tex]
Thus,
The correct value of k[p(x)] for given context is given by: Option b. k[p(x)] = 5x − 28
Learn more about composite functions here:
https://brainly.com/question/24780056
