For the pair of functions, find the indicated composition.
-$f ( x ) = x ^ { 4 } + 5 , g ( x ) = \sqrt [ 4 ] { x - 5 }$
Find $( g \circ f ) ( x )$
A) x
B) $| x |$
C) $x ^ { 4 }$
D) -x

Question

For the pair of functions, find the indicated composition.
-$f ( x ) = x ^ { 4 } + 5 , g ( x ) = \sqrt [ 4 ] { x - 5 }$
Find $( g \circ f ) ( x )$
A)  x 
B) $| x |$
C) $x ^ { 4 }$
D)  -x

Quizplus · Accepted Answer

To find $(g \circ f)(x)$, we first apply $f(x)$, then apply $g$ to the result of $f(x)$. So, $f(x) = x^4 + 5$. Applying $g$ to $f(x)$, we get $g(f(x)) = \sqrt[4]{x^4 + 5 - 5} = \sqrt[4]{x^4} = x$.

For the Pair of Functions, Find the Indicated Composition f(x)=x4+5,g(x)=x−54f ( x ) = x ^ { 4 } + 5 , g ( x ) = \sqrt [ 4 ] { x - 5 }f(x)=x4+5,g(x)=4x−5​

For the Pair of Functions, Find the Indicated Composition $f ( x ) = x ^ { 4 } + 5 , g ( x ) = \sqrt [ 4 ] { x - 5 }$