f(n)= -4n + 1 g(n)= -2n - 5Find (f∘g)

Nayeon Mina

Nayeon Mina

Answered question

2022-09-27

f(n)= -4n + 1 

g(n)= -2n - 5

Find (f∘g) (n) 

Answer & Explanation

madeleinejames20

madeleinejames20

Skilled2023-05-25Added 165 answers

Given:
f(n)=4n+1
g(n)=2n5
To find (f*g)(n), we substitute g(n) into f(n) wherever we see n.
Let's start by substituting g(n) into f(n):
(f*g)(n)=f(g(n))
Replace n in f(n) with g(n):
(f*g)(n)=4(g(n))+1
Now, substitute the expression for g(n):
(f*g)(n)=4(2n5)+1
To simplify the expression, we distribute the -4 to each term within the parentheses:
(f*g)(n)=8n+20+1
Combine like terms:
(f*g)(n)=8n+21
Therefore, the composition of the functions f(n) and g(n), denoted as (f*g)(n), is given by:
(f*g)(n)=8n+21

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