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 $f$. Here, $g(x) = x + 3$, so applying $f$ to $g(x)$ gives $f(g(x)) = |x + 3|$. The domain of $f \circ g$ is all real numbers because adding 3 to any real number and then taking the absolute value does not restrict the domain.

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 $f ( x ) = | x | , g ( x ) = x + 3$