Determine whether (f  g)(x) = x and whether (g  f)(x) = x.
-$$f ( x ) = \sqrt [ 5 ] { x - 14 } , g ( x ) = x ^ { 5 } + 14$$
A) No, no
B) No, yes
C) Yes, yes
D) Yes, no

Question

Quizplus · Accepted Answer

The composition (f ∘ g)(x) = f(g(x)) = f(x^5 + 14) = √[5]{(x^5 + 14) - 14} = x, and (g ∘ f)(x) = g(f(x)) = g(√[5]{x - 14}) = (√[5]{x - 14})^5 + 14 = x - 14 + 14 = x.

Determine Whether (F  G)(x) = X and Whether (G f(x)=x−145,g(x)=x5+14f ( x ) = \sqrt [ 5 ] { x - 14 } , g ( x ) = x ^ { 5 } + 14f(x)=5x−14​,g(x)=x5+14

Determine Whether (F  G)(x) = X and Whether (G $f ( x ) = \sqrt [ 5 ] { x - 14 } , g ( x ) = x ^ { 5 } + 14$