228k views
5 votes
Given the functions: f(x) = x^3, g(x) = x - 7, h(x) = x + 2, which composition of functions would

give you the new function n(x) = (x + 2)^3– 7?


A. n(x) = f(g(h(x)))

B. n(x) = g(f(h(x)))

C. n(x) = g(h(f(x)))

D. n(x) = h(f(g(x)))

E. n(x) = f(h(g(x)))

please help a girl is struggling❤️

1 Answer

7 votes

Answer:

n(x) = g(f(h(x)))

Explanation:

Given


f(x) = x^3


g(x) = x-7


h(x) = x + 2

Required

Which function represents
n(x) = (x + 2)^3 - 7

Start by solving for f(h(x)):

Given that:


f(x) = x^3 and
h(x) = x + 2

Substitute x + 2 for the x in f(x)


f(h(x)) = (x + 2)^3

Next, solve for g(f(h(x)))

Given that:


g(x) = x-7 and
f(h(x)) = (x + 2)^3

Substitute (x + 2)^3 for the x in g(x)


g(f(h(x))) = (x + 2)^3 - 7

Recall that:


n(x) = (x + 2)^3 - 7

Hence:


n(x) = g(f(h(x))) = (x + 2)^3 - 7

User Lutti Coelho
by
7.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories