Let $f ( x ) = \sqrt { x } , g ( x ) = x + 2$. Find the composite function which expresses the given correspondence correctly.
$\sqrt [ 4 ] { x }$
A) $\quad ( g \circ g ) ( x )$
B) $( f \circ f ) ( x )$
C) $\quad ( g \circ f ) ( x )$
D) $\quad ( f \circ g ) ( x )$
E) none of the above

Question

Quizplus · Accepted Answer

$( f \circ f ) ( x )$ means applying $f$ twice. Since $f(x) = \sqrt{x}$, applying it twice gives $\sqrt{\sqrt{x}} = \sqrt[4]{x}$, which matches the given correspondence.

Let f(x)=x,g(x)=x+2f ( x ) = \sqrt { x } , g ( x ) = x + 2f(x)=x​,g(x)=x+2

Let $f ( x ) = \sqrt { x } , g ( x ) = x + 2$