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

The composite function $f \circ g$ means applying $g$ first and then $f$, so $f(g(x)) = f(x^2) = \sqrt{x^2 + 5}$. The domain of $f \circ g$ is all real numbers because $x^2$ is defined for all real numbers, and adding 5 to any square keeps the argument of the square root non-negative.

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 $f ( x ) = \sqrt { x + 5 } , g ( x ) = x ^ { 2 }$