Find $g \circ f$ and the domain of the composite function.
$f ( x ) = x ^ { 2 } + 4 , g ( x ) = \sqrt { x }$

A) $( x + 4 ) ^ { 4 }$ Domain of $g \circ f$ : all real numbers x
B) $( x - 4 ) ^ { 4 }$ Domain of $g \circ f$ : all real numbers x
C) $\sqrt { x ^ { 2 } + 4 }$ Domain of $g \circ f$ : all real numbers x
D) $\sqrt { ( x - 4 ) ^ { 4 } }$ Domain of $g \circ f$ : all real numbers x
E) $\sqrt { ( x + 4 ) ^ { 4 } }$ Domain of $g \circ f$ : all real numbers x

Question

Find $g \circ f$ and the domain of the composite function. 
 $f ( x ) = x ^ { 2 } + 4 , g ( x ) = \sqrt { x }$

A) $( x + 4 ) ^ { 4 }$ Domain of $g \circ f$ : all real numbers x
B) $( x - 4 ) ^ { 4 }$ Domain of $g \circ f$ : all real numbers x
C) $\sqrt { x ^ { 2 } + 4 }$ Domain of $g \circ f$ : all real numbers x
D) $\sqrt { ( x - 4 ) ^ { 4 } }$ Domain of $g \circ f$ : all real numbers x
E) $\sqrt { ( x + 4 ) ^ { 4 } }$ Domain of $g \circ f$ : all real numbers x

Quizplus · Accepted Answer

The composite function $g \circ f$ means applying $f$ first and then $g$, so we first calculate $f(x) = x^2 + 4$ and then apply $g$ to the result, which gives $g(f(x)) = \sqrt{x^2 + 4}$. The domain of this composite function is all real numbers because $x^2 + 4$ is always positive, making the square root defined for all real $x$.

Find g∘fg \circ fg∘f And the Domain of the Composite Function f(x)=x2+4,g(x)=xf ( x ) = x ^ { 2 } + 4 , g ( x ) = \sqrt { x }f(x)=x2+4,g(x)=x​

Find $g \circ f$ And the Domain of the Composite Function $f ( x ) = x ^ { 2 } + 4 , g ( x ) = \sqrt { x }$