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.

Question

Mathematics

Henry Krause

17 August, 15:01

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.

+3

Answers (1)

Know the Answer?

Mylee Horne · Answer 1

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