Find $g \circ f$ and the domain of the composite function. $f ( x ) = | x | , g ( x ) = x + 4$
A) $| x - 4 |$ Domain of $g \circ f$ : all real numbers x
B) $x - | 4 |$ Domain of $g \circ f$ : all real numbers x
C) $| x | - 4$ Domain of $g \circ f$ : all real numbers x
D) $| x | + 4$ Domain of $g \circ f$ : all real numbers x
E) $| x + 4 |$ Domain of $g \circ f$ : all real numbers x

Question

Find $g \circ f$ and the domain of the composite function.​ $f ( x ) = | x | , g ( x ) = x + 4$ ​ ​
A) $| x - 4 |$ Domain of $g \circ f$ : all real numbers x
B) $x - | 4 |$ Domain of $g \circ f$ : all real numbers x
C) $| x | - 4$ Domain of $g \circ f$ : all real numbers x
D) $| x | + 4$ Domain of $g \circ f$ : all real numbers x
E) $| x + 4 |$ Domain of $g \circ f$ : all real numbers x

Quizplus · Accepted Answer

The only difference between the two expressions is in the third block of characters (6f71 vs. 6f72). Since this difference indicates a change in the function itself, it means we are dealing with a composite function. The domain of the composite function will be the domain of the function with the smallest domain, which is 11ea99db_b6cd_0bba_94ac_3542f9551773_TB4590_11. Therefore, the answer is D.

Find g∘fg \circ fg∘f And the Domain of the Composite Function f(x)=∣x∣,g(x)=x+4f ( x ) = | x | , g ( x ) = x + 4f(x)=∣x∣,g(x)=x+4

Find $g \circ f$ And the Domain of the Composite Function $f ( x ) = | x | , g ( x ) = x + 4$