MATHEMATICS HIGH SCHOOL

Given the functions k(x) = 5x − 8 and p(x) = x − 4, solve k[p(x)] and select the correct answer below.a. k[p(x)] = 5x − 12
b. k[p(x)] = 5x − 28
c. k[p(x)] = 5x2 − 12
d. k[p(x)] = 5x2 − 28

Answers

Answer 1
Answer:

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

What are function of functions and how are they represented?

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

(f\circ g)(x)

where the x is the input to first function.

Thus, we have;

(f\circ g)(x) = f(g(x))

For given context, the functions are:

k(x) = 5x - 8 \np(x) = x - 4,

Composing them to get k[p(x)], we need to put whatever p(x) output as input to k(x).
Thus,

k(p(x)) = 5(p(x)) - 8\n\nk(p(x)) = 5(x-4) - 8 = 5x - 20 - 8 = 5x - 28\n

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:

brainly.com/question/24780056
Answer 2
Answer:

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 .

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A sine function can be used to model light waves. Green light has a wave length, or period of about 520 nm. Which equation best models green light?A.) y=sin 260/pi theta

B.) y= sin pi/520 theta

C.) y= sin 520/pi theta

D.) y= sin pi/260 theta


Please help

Answers

Answer:

y = A sin (kx \pm wt)

Where k represent the number of wave k =(2\pi)/(\lambda) and w =(2\pi)/(T) represent the angular frequency with T the period.

For this case we know tha T = 520 nm

And the angular frequency would be given by:

w = (2\pi)/(520)= (pi)/(260)

So then the possible anwer for this case would be:

D.) y= sin pi/260 theta

Since is the only option with satisfy the general equation of a wave.

Step-by-step explanation:

Since the sine function can be used to model light waves we can use the following general expression:

y = A sin (kx \pm wt)

Where k represent the number of wave k =(2\pi)/(\lambda) and w =(2\pi)/(T) represent the angular frequency with T the period.

For this case we know tha T = 520 nm

And the angular frequency would be given by:

w = (2\pi)/(520)= (pi)/(260)

So then the possible anwer for this case would be:

D.) y= sin pi/260 theta

Since is the only option with satisfy the general equation of a wave.

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