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10 October, 01:09

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.

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  1. 10 October, 04:34
    0
    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.
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