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
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