Determine whether $$( f \circ g ) ( x ) = x \text { and whether } ( g \circ f ) ( x ) = x \text {. }$$
-$f ( x ) = \sqrt [ 5 ] { x - 6 } , g ( x ) = x ^ { 5 } + 6$
A) No, no
B) No, yes
C) Yes, no
D) Yes, yes

Name: Determine whether \[( f \circ g ) ( x ) = x \text { and whether } ( g \circ f ) ( x ) = x \text {. }\] -$f ( x ) = \sqrt [ 5 ] { x - 6 } , g ( x ) = x ^ { 5 } + 6$ A) No, no B) No, yes C) Yes, no D) Yes, yes
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Quizplus · Accepted Answer

Both compositions simplify to $x$, showing that $f$ and $g$ are inverses.

Determine Whether (f∘g)(x)=x and whether (g∘f)(x)=x. ( f \circ g ) ( x ) = x \text { and whether } ( g \circ f ) ( x ) = x \text {. }(f∘g)(x)=x and whether (g∘f)(x)=x.

Determine Whether $( f \circ g ) ( x ) = x \text { and whether } ( g \circ f ) ( x ) = x \text {. }$