g(n) = -4n -4 h(n) =n²+5+nFind (g∘h) (n) 

Nayeon Mina

Nayeon Mina

Answered question

2022-09-27

g(n) = -4n -4

 h(n) =n²+5+n

Find (g∘h) (n) 

Answer & Explanation

madeleinejames20

madeleinejames20

Skilled2023-05-25Added 165 answers

To solve the problem, we need to find the composition of the functions g(n) and h(n), denoted as (g*h)(n).
Given:
g(n)=4n4
h(n)=n2+5+n
To find (g*h)(n), we substitute h(n) into g(n) wherever we see n.
Let's start by substituting h(n) into g(n):
(g*h)(n)=g(h(n))
Replace n in g(n) with h(n):
(g*h)(n)=4(h(n))4
Now, substitute the expression for h(n):
(g*h)(n)=4(n2+5+n)4
To simplify the expression, we distribute the -4 to each term within the parentheses:
(g*h)(n)=4n2204n4
Combining like terms:
(g*h)(n)=4n24n24
Therefore, the composition of the functions g(n) and h(n), denoted as (g*h)(n), is given by:
(g*h)(n)=4n24n24

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