Asked by Marish Quilicot on May 21, 2024
Verified
Find (g∘f) (x) ( g \circ f ) ( x ) (g∘f) (x) where f(x) =4x+7f ( x ) = 4 x + 7f(x) =4x+7 and g(x) =x2−1g ( x ) = x ^ { 2 } - 1g(x) =x2−1 .
A) 4x328x2−4x−74 x ^ { 3 } 28 x ^ { 2 } - 4 x - 74x328x2−4x−7
B) 4x2+34 x ^ { 2 } + 34x2+3
C) 16x2+56x+4816 x ^ { 2 } + 56 x + 4816x2+56x+48
D) 16x2+616 x ^ { 2 } + 616x2+6
E) 4x2+64 x ^ { 2 } + 64x2+6
Composition
The operation of applying one function to the result of another to produce a third function.
Function
An arrangement between inputs and a cadre of sanctioned outputs, in which every input is designated a specific output.
- Comprehend and utilize the principle of function composition in order to determine \((g \circ f)(x)\) and \((f \circ g)(x)\).
Verified Answer
SB
SUSHANT BISTAMay 22, 2024
Final Answer :
C
Explanation :
To find (g∘f)(x)(g \circ f)(x)(g∘f)(x) , first apply f(x)f(x)f(x) and then apply g(x)g(x)g(x) to the result. Substituting f(x)=4x+7f(x) = 4x + 7f(x)=4x+7 into g(x)=x2−1g(x) = x^2 - 1g(x)=x2−1 , we get g(f(x))=(4x+7)2−1g(f(x)) = (4x + 7)^2 - 1g(f(x))=(4x+7)2−1 . Expanding this gives 16x2+56x+49−1=16x2+56x+4816x^2 + 56x + 49 - 1 = 16x^2 + 56x + 4816x2+56x+49−1=16x2+56x+48 .
Learning Objectives
- Comprehend and utilize the principle of function composition in order to determine \((g \circ f)(x)\) and \((f \circ g)(x)\).