A. (F∘G)(X) = 4x + 4 ;
B. (G∘F)(X) = 4x +10 ;
C. (F∘G)(−1) = 0;
D. (G∘F)(−1) = 6.
Let's break down each part:
A. (F∘G)(X):
This is the composition of functions F and G. To find it, substitute G(X) into F(X):
(F∘G)(X)=F(G(X))=F(4X+2)=(4X+2)+2=4X+4
B. (G∘F)(X):
Similarly, substitute F(X) into G(X):
(G∘F)(X)=G(F(X))=G(X+2)=4(X+2)+2=4X+10
C. (F∘G)(−1):
Replace X with -1 in the expression we found for (F∘G)(X):
(F∘G)(−1)=4(−1)+4= 0
D. (G∘F)(−1):
Replace X with -1 in the expression we found for (G∘F)(X):
(G∘F)(−1)=4(−1)+10= 6
Question
For F(X)=X+2 And G(X)=4x+2, Find The Following Functions. A. (F∘G)(X);B.(G∘F)(X);C.(F∘G)(−1);D.(G∘F)(−1)