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For the functions f(x) = 2x + 2 and g(x) = 7x + 1, which composition produces the greatest output?

Both compositions produce the same output.
Neither composition produces an output.
f(g(x)) produces the greatest output.
g(f(x)) produces the greatest output.

Respuesta :

First we have to find (f o g)(x):
(f o g)(x) = [2(7x + 1) + 2] = (14x + 2 + 2) = 14x + 4 
Then we have to find (g o f)(x):
(g o f)(x) = [7(2x + 2) + 1] = (14x + 14 + 1) = 14x + 15 
Comparing both the results:

(g o f)(x) > (f o g)(x)
According to above explanation,
D.g(f(x)) produces the greatest output, is the correct answer.
Nonportrit

The answer is the fourth option "g(f(x)) produces the greatest output."

How:

  • [tex] (f o g)(x) = [2(7x + 1) + 2] = (14x + 2 + 2) = 14x + 4 [/tex]
  • [tex] (g o f)(x) = [7(2x + 2) + 1] = (14x + 14 + 1) = 14x + 15 [/tex]

Looking at both equations you would see that (g o f)(x) > (f o g)(x) so the answer is the fourth option!

Hope this helps!