Question

For the functions f(x) = 2x + 3 and g(x) = 6x + 2, which composition produces the greatest output?

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

Answer 1

Given:
f(x) = 2x + 3
g(x) = 6x + 2

Therefore
(f.g)(x) = 2(6x+2) + 3 = 12x + 7
This is a straight line with slope = 12, and y-intercept = 7.

(g.f)(x) = 6(2x+3) + 2 = 12x + 20
This is a straight line with slope = 12 and y-intercept = 20.

The two compositions represent straight lines with a slope of 12.
Because (g.f)(x) has a higher intercept, it produces the greatest output.

Answer:
g(f(x)) produces the greatest output.