Find $f \circ g$ and the domain of the composite function.
$f ( x ) = \sqrt { x + 5 } , g ( x ) = x ^ { 2 }$

A) $( x + 5 ) ^ { 2 }$ Domain of $f \circ g$ : all real numbers x
B) $\sqrt { x ^ { 2 } + 5 }$ Domain of $f \circ g$ : all real numbers x
C) $- \sqrt { ( x + 5 ) ^ { 2 } }$ Domain of $f \circ g$ : all real numbers x
D) $( x - 5 ) ^ { 2 }$ Domain of $f \circ g$ : all real numbers x
E) $\sqrt { ( x - 5 ) ^ { 2 } }$ Domain of $f \circ g$ : all real numbers x

Question

Find $f \circ g$ and the domain of the composite function. 
 $f ( x ) = \sqrt { x + 5 } , g ( x ) = x ^ { 2 }$

A) $( x + 5 ) ^ { 2 }$ Domain of $f \circ g$ : all real numbers x
B) $\sqrt { x ^ { 2 } + 5 }$ Domain of $f \circ g$ : all real numbers x
C) $- \sqrt { ( x + 5 ) ^ { 2 } }$ Domain of $f \circ g$ : all real numbers x
D) $( x - 5 ) ^ { 2 }$ Domain of $f \circ g$ : all real numbers x
E) $\sqrt { ( x - 5 ) ^ { 2 } }$ Domain of $f \circ g$ : all real numbers x

Quizplus · Accepted Answer

To find $f \circ g$, we substitute $g(x) = x^2$ into $f(x)$, resulting in $f(g(x)) = \sqrt{x^2 + 5}$. The domain of this composite function is all real numbers because $x^2$ is defined for all real numbers, and adding 5 to any square keeps the radicand non-negative, allowing for real square roots.

Find f∘gf \circ gf∘g And the Domain of the Composite Function f(x)=x+5,g(x)=x2f ( x ) = \sqrt { x + 5 } , g ( x ) = x ^ { 2 }f(x)=x+5​,g(x)=x2

Find $f \circ g$ And the Domain of the Composite Function $f ( x ) = \sqrt { x + 5 } , g ( x ) = x ^ { 2 }$