Question

For the functions f(x) = 2x + 2 and g(x) = 7x + 1, which composition produces the greatest output? a) Both compositions produce the same output. b) Neither composition produces an output. c) f(g(x)) produces the greatest output. d) g(f(x)) produces the greatest output.

Answer 1

D is the correct answer

Answer 2

so subsitue and try so
f(g(x))=2(7x+1)+2
g(f(x))=7(2x+2)+1

multiply them out
f(g(x))=2(7x+1)+2=14x+2+2=14x+4
g(f(x))=7(2x+2)+1=14x+14+1=14x+15
14x+15>14x+4
therefor
g(f(x))>f(g(x))

the answer is D g(f(x)) produces the greatest output