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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❤️

Respuesta :

MrRoyal

Answer:

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

Step-by-step explanation:

Given

[tex]f(x) = x^3[/tex]

[tex]g(x) = x-7[/tex]

[tex]h(x) = x + 2[/tex]

Required

Which function represents [tex]n(x) = (x + 2)^3 - 7[/tex]

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

Given that:

[tex]f(x) = x^3[/tex]  and [tex]h(x) = x + 2[/tex]

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

[tex]f(h(x)) = (x + 2)^3[/tex]

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

Given that:

[tex]g(x) = x-7[/tex] and [tex]f(h(x)) = (x + 2)^3[/tex]

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

[tex]g(f(h(x))) = (x + 2)^3 - 7[/tex]

Recall that:

[tex]n(x) = (x + 2)^3 - 7[/tex]

Hence:

[tex]n(x) = g(f(h(x))) = (x + 2)^3 - 7[/tex]

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