Find gof and the domain of composite function.
$f ( x ) = x ^ { 2 } + 5 , \quad g ( x ) = \sqrt { x }$
A) $\sqrt { ( x - 5 ) ^ { 5 } }$
Domain of $g \circ f$ : all real numbers $x$
B) $( x + 5 ) ^ { 5 }$
Domain of $g o f$ : all real numbers $x$
C) $\sqrt { ( x + 5 ) ^ { 5 } }$
Domain of $g \circ f$ : all real numbers $x$
D) $( x - 5 ) ^ { 5 }$
Domain of $g \circ f$ : all real numbers $x$
E) $\sqrt { x ^ { 2 } + 5 }$
Domain of $g o f$ : all real numbers $x$

Question

Find gof and the domain of composite function. 
$f ( x ) = x ^ { 2 } + 5 , \quad g ( x ) = \sqrt { x }$
A) $\sqrt { ( x - 5 ) ^ { 5 } }$
Domain of $g \circ f$ : all real numbers $x$
B) $( x + 5 ) ^ { 5 }$
Domain of $g o f$ : all real numbers $x$
C) $\sqrt { ( x + 5 ) ^ { 5 } }$
Domain of $g \circ f$ : all real numbers $x$
D) $( x - 5 ) ^ { 5 }$
Domain of $g \circ f$ : all real numbers $x$
E) $\sqrt { x ^ { 2 } + 5 }$
Domain of $g o f$ : all real numbers $x$

Quizplus · Accepted Answer

To find $g \circ f$, we need to plug in $f(x)$ into the function $g$: $g(f(x))=\sqrt{f(x)}=\sqrt{x^2+5}$. The domain of this composite function is all real numbers $x$, since the square root function is defined for all non-negative numbers. Therefore, the correct choice is E.

Find Gof and the Domain of Composite Function f(x)=x2+5,g(x)=xf ( x ) = x ^ { 2 } + 5 , \quad g ( x ) = \sqrt { x }f(x)=x2+5,g(x)=x​

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