Asked by Tiffany Batura on Mar 10, 2024
Verified
Find (f∘g) (x) ( f \circ g ) ( x ) (f∘g) (x) where f(x) =4x−3f ( x ) = 4 x - 3f(x) =4x−3 and g(x) =x+8g ( x ) = \sqrt { x + 8 }g(x) =x+8 .
A) 4x+8−34 \sqrt { x + 8 } - 34x+8−3
B) 4x+5\sqrt { 4 x + 5 }4x+5
C) 4x+32−3\sqrt { 4 x + 32 } - 34x+32−3
D) 4x+54 \sqrt { x + 5 }4x+5
E) (4x−3) x+8( 4 x - 3 ) \sqrt { x + 8 }(4x−3) x+8
A) 4x+8−34 \sqrt { x + 8 } - 34x+8−3
B) 4x+5\sqrt { 4 x + 5 }4x+5
C) 4x+32−3\sqrt { 4 x + 32 } - 34x+32−3
D) 4x+54 \sqrt { x + 5 }4x+5
E) (4x−3) x+8( 4 x - 3 ) \sqrt { x + 8 }(4x−3) x+8
Composition
In mathematics, composition refers to the application of one function to the results of another, denoted as \(f(g(x))\), where \(g\) is applied first and then \(f\).
Function
A connection framework between a pack of inputs and a slew of endorsed outputs, ensuring each input leads to a distinct output.
- Analyze specific values within composite functions.
Verified Answer
TM
Timothy Michalek
Mar 10, 2024
Final Answer :
A
Explanation :
The composition (f∘g)(x)( f \circ g ) ( x )(f∘g)(x) means applying ggg first and then fff . So, first, we calculate g(x)=x+8g(x) = \sqrt{x + 8}g(x)=x+8 , and then apply fff to this result: f(g(x))=4(x+8)−3f(g(x)) = 4(\sqrt{x + 8}) - 3f(g(x))=4(x+8)−3 , which matches choice A.
Learning Objectives
- Analyze specific values within composite functions.