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Ivahew [28]
2 years ago
5

Express your answer as a polynomial in standard form

Mathematics
1 answer:
Bingel [31]2 years ago
8 0

Answer:

f(g(x)) = 4x² + 16x + 13

Step-by-step explanation:

Given the composition of functions f(g(x)), for which f(x) = 4x + 5, and g(x) = x² + 4x + 2.

<h3><u>Definitions:</u></h3>
  • The <u>polynomial in standard form</u> has terms that are arranged by <em>descending</em> order of degree.
  • In the <u>composition of function</u><em> f  </em>with function <em>g</em><em>, </em>which is alternatively expressed as <em>f  </em>° <em>g,</em> is defined as (<em>f </em> ° <em>g</em>)(x) = f(g(x)).

In evaluating composition of functions, the first step is to evaluate the inner function, g(x). Then, we must use the derived value from g(x) as an input into f(x).

<h3><u>Solution:</u></h3>

Since we are not provided with any input values to evaluate the given composition of functions, we can express the given functions as follows:

f(x) = 4x + 5

g(x) = x² + 4x + 2

f(g(x)) = 4(x² + 4x + 2)  + 5

Next, distribute 4 into the parenthesis:

f(g(x)) = 4x² + 16x + 8  + 5

Combine constants:

f(g(x)) = 4x² + 16x + 13

Therefore, f(g(x)) as a polynomial in <em>x</em> that is written in standard form is: 4x² + 16x + 13.

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