Determine whether (f ∘ g)(x) = x and whether (g ∘ f)(x) = x.
-$$f ( x ) = x ^ { 3 } + 7 , g ( x ) = \sqrt [ 3 ] { x - 7 }$$
A) Yes, no
B) No, yes
C) No, no
D) Yes, yes

Question

Quizplus · Accepted Answer

(f ∘ g)(x) = f(g(x)) = f(√[3]{x - 7}) = (√[3]{x - 7})^3 + 7 = x - 7 + 7 = x, so (f ∘ g)(x) = x. (g ∘ f)(x) = g(f(x)) = g(x^3 + 7) = √[3]{(x^3 + 7) - 7} = √[3]{x^3} = x, so (g ∘ f)(x) = x.

Determine Whether (F ∘ G)(x) = X and Whether (G f(x)=x3+7,g(x)=x−73f ( x ) = x ^ { 3 } + 7 , g ( x ) = \sqrt [ 3 ] { x - 7 }f(x)=x3+7,g(x)=3x−7​

Determine Whether (F ∘ G)(x) = X and Whether (G $f ( x ) = x ^ { 3 } + 7 , g ( x ) = \sqrt [ 3 ] { x - 7 }$