Question

Find [fog](x)and [gof](x)

F(X)=X2+2X and g(x)=x-9
The zeros in the middle are supposed br small o
A. F[g(x)=x2-16x+81; g[f(x)=x2+3x-9
B. F[g(x)=x2+2x+81; g[f(x)=x2+2x-9
C. F[g(x)=x2-16x+63; g [f(x)=x2+2x-9
D. F[g(x)=x2+2x+81; g [f(x)=x2+3x-9

Answer 1

f(x)=x^2+2x
g(x)=x-9

(f o g)(x)=f(g(x))=f(x-9)=(x-9)^2+2(x-9)=(x)^2-2(x)(9)+(9)^2+2x-18
(f o g)(x)=f(g(x))=x^2-18x+81+2x-18
(f o g)(x)=f(g(x)=x^2-16x+63

(g o f)(x)=g(f(x))=g(x^2+2x)=(x^2+2x)-9
(g o f)(x)=g(f(x))=x^2+2x-9

Answer: Option C. F[g(x)]=x^2-16x+63; g [f(x)]=x^2+2x-9