Find $f \circ g$ and the domain of the composite function.
$f ( x ) = | x | , g ( x ) = x + 3$

A) $\left| ( x - 3 ) ^ { 3 } \right|$ Domain of $f \circ g$ : all real numbers x
B) $\sqrt { ( x + 3 ) ^ { 3 } }$ Domain of $f \circ g$ : all real numbers x
C) $| x + 3 |$ Domain of $f \circ g$ : all real numbers x
D) $\left| ( x + 3 ) ^ { 3 } \right|$ Domain of $f \circ g$ : all real numbers x
E) $| x - 3 |$ Domain of $f \circ g$ : all real numbers x

Question

Find $f \circ g$ and the domain of the composite function. 
 $f ( x ) = | x | , g ( x ) = x + 3$

A) $\left| ( x - 3 ) ^ { 3 } \right|$ Domain of $f \circ g$ : all real numbers x
B) $\sqrt { ( x + 3 ) ^ { 3 } }$ Domain of $f \circ g$ : all real numbers x
C) $| x + 3 |$ Domain of $f \circ g$ : all real numbers x
D) $\left| ( x + 3 ) ^ { 3 } \right|$ Domain of $f \circ g$ : all real numbers x
E) $| x - 3 |$ Domain of $f \circ g$ : all real numbers x

Quizplus · Accepted Answer

The composite function $f \circ g$ means applying $g$ first and then $f$. Given $g(x) = x + 3$, applying $f$ to $g(x)$ results in $f(g(x)) = |x + 3|$. The domain of $f \circ g$ is all real numbers because both the absolute value function and the linear function have domains of all real numbers.

Find f∘gf \circ gf∘g And the Domain of the Composite Function f(x)=∣x∣,g(x)=x+3f ( x ) = | x | , g ( x ) = x + 3f(x)=∣x∣,g(x)=x+3

Find $f \circ g$ And the Domain of the Composite Function $f ( x ) = | x | , g ( x ) = x + 3$