Decide whether the composite functions, f ° g and g ° f, are equal to x.
-$$f ( x ) = x ^ { 3 } + 1 , g ( x ) = \sqrt [ 3 ] { x - 1 }$$
A) No, yes
B) No, no
C) Yes, yes
D) Yes, no

Question

Quizplus · Accepted Answer

The composite functions f ° g and g ° f both simplify to x. For f ° g, substituting g(x) into f(x) gives f(g(x)) = ((x - 1)^(1/3))^3 + 1 = x - 1 + 1 = x. For g ° f, substituting f(x) into g(x) gives g(f(x)) = ((x^3 + 1) - 1)^(1/3) = x^3^(1/3) = x.

Decide Whether the Composite Functions, F ° G and G f(x)=x3+1,g(x)=x−13f ( x ) = x ^ { 3 } + 1 , g ( x ) = \sqrt [ 3 ] { x - 1 }f(x)=x3+1,g(x)=3x−1​

Decide Whether the Composite Functions, F ° G and G $f ( x ) = x ^ { 3 } + 1 , g ( x ) = \sqrt [ 3 ] { x - 1 }$