Math Problem Statement

Orville composed functions f(x)=4x−−√3−2f(x)=4x3−2 and g(x)=(x+24)3g(x)=(x+24)3 to see if the two functions are inverses of each other. His work is shown below.

f∘g=f(g(x))f∘g=f(g(x)) f∘g=f((x+24)3)f∘g=f((x+24)3) f∘g=4(x+24)3−−−−−−√3−2f∘g=4(x+24)33−2 f∘g=4(x+24)−2f∘g=4(x+24)−2 f∘g=(x+2)−2f∘g=(x+2)−2 f∘g=xf∘g=x

Which of the following is true about Orville’s work?

Select THREE correct answers.

A.Orville’s work is correct.

B.Orville’s work is not correct.

C.Orville’s work indicates that the functions are inverses.

D.Orville’s work indicates that the functions are not inverses.

E.The two functions ff and gg are inverses

F.The two functions ff and gg are not inverses.

Solution

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Math Problem Analysis

Mathematical Concepts

Function Composition
Inverse Functions
Algebra

Formulas

f(g(x)) = 4√3(g(x))−2
g(f(x)) = (f(x) + 24)^3
Inverse function property: f(g(x)) = x and g(f(x)) = x

Theorems

Inverse Function Theorem

Suitable Grade Level

Grades 9-11