Answered

Westonci.ca makes finding answers easy, with a community of experts ready to provide you with the information you seek. Join our platform to connect with experts ready to provide precise answers to your questions in different areas. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

Select the correct answer.

Consider this function:
[tex]\[ f(x) = -4x + 7 \][/tex]

Which polynomial is equivalent to [tex]\[ f(f(x)) \][/tex]?

A. [tex]\[ 16x - 28 \][/tex]

B. [tex]\[ 16x^2 - 56x + 49 \][/tex]

C. [tex]\[ 16x - 21 \][/tex]

D. [tex]\[ 16x^2 - 56x + 56 \][/tex]

Sagot :

GinnyAnswer
To solve the problem, we need to compute the composition of the function [tex]\( f \)[/tex] with itself, i.e., [tex]\( f(f(x)) \)[/tex]. The given function is:

[tex]\[ f(x) = -4x + 7 \][/tex]

First, we substitute [tex]\( f(x) \)[/tex] into the function itself:

[tex]\[ f(f(x)) = f(-4x + 7) \][/tex]

Next, we evaluate [tex]\( f(-4x + 7) \)[/tex] by substituting [tex]\( -4x + 7 \)[/tex] for [tex]\( x \)[/tex] in [tex]\( f(x) \)[/tex]:

[tex]\[ f(-4x + 7) = -4(-4x + 7) + 7 \][/tex]

Now, we need to simplify the expression:

[tex]\[ f(-4x + 7) = -4(-4x) + (-4)(7) + 7 \][/tex]
[tex]\[ f(-4x + 7) = 16x - 28 + 7 \][/tex]
[tex]\[ f(-4x + 7) = 16x - 21 \][/tex]

Therefore, the polynomial equivalent to [tex]\( f(f(x)) \)[/tex] is:

[tex]\[ f(f(x)) = 16x - 21 \][/tex]

Among the given options, the correct answer is:

C. [tex]\( 16x - 21 \)[/tex]
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.