Determine whether (f ∘ g)(x) = x and whether (g ∘ f)(x) = x.
-$$f ( x ) = \sqrt [ 5 ] { x - 7 } , g ( x ) = x ^ { 5 } + 7$$
A) Yes, no
B) Yes, yes
C) No, no
D) No, yes

Question

Quizplus · Accepted Answer

(f ∘ g)(x) = f(g(x)) = f(x^5 + 7) = √[5]{(x^5 + 7) - 7} = √[5]{x^5} = x.  (g ∘ f)(x) = g(f(x)) = g(√[5]{x - 7}) = (√[5]{x - 7})^5 + 7 = x - 7 + 7 = x.

Determine Whether (F ∘ G)(x) = X and Whether (G f(x)=x−75,g(x)=x5+7f ( x ) = \sqrt [ 5 ] { x - 7 } , g ( x ) = x ^ { 5 } + 7f(x)=5x−7​,g(x)=x5+7

Determine Whether (F ∘ G)(x) = X and Whether (G $f ( x ) = \sqrt [ 5 ] { x - 7 } , g ( x ) = x ^ { 5 } + 7$