Asked by Daniel Carrera Chavarria on May 17, 2024
Verified
Find the domain of g∘fg \circ fg∘f where f(x) =x−2f ( x ) = \sqrt { x - 2 }f(x) =x−2 and g(x) =x+6g ( x ) = x + 6g(x) =x+6 .
A) [2,∞) [ 2 , \infty ) [2,∞)
B) [4,∞) [ 4 , \infty ) [4,∞)
C) [−4,∞) [ - 4 , \infty ) [−4,∞)
D) [−6,∞) [ - 6 , \infty ) [−6,∞)
E) [0,∞) [ 0 , \infty ) [0,∞)
Domain
The collection of all potential entry points that a function can accept.
Composition
The combining of two or more functions by applying one function to the result of another, indicated as \(f(g(x))\).
- Establish the set of all possible inputs for composite functions.
Verified Answer
MB
Meghan BryantMay 20, 2024
Final Answer :
A
Explanation :
The domain of g∘fg \circ fg∘f is determined by the domain of f(x)f(x)f(x) , since f(x)f(x)f(x) must be evaluated before applying g(x)g(x)g(x) . For f(x)=x−2f(x) = \sqrt{x - 2}f(x)=x−2 , the expression under the square root must be non-negative, so x−2≥0x - 2 \geq 0x−2≥0 , which simplifies to x≥2x \geq 2x≥2 . Therefore, the domain of g∘fg \circ fg∘f is [2,∞)[2, \infty)[2,∞) .
Learning Objectives
- Establish the set of all possible inputs for composite functions.