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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

Blair Lewis

in Mathematics

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Ashley Howard on November 29, 2018

Given:f(x) = 2x + 3 g(x) = 6x + 2Therefore(f.g)(x) = 2(6x+2) + 3 = 12x + 7This is a straight line with slope = 12, and y-intercept = 7.(g.f)(x) = 6(2x+3) + 2 = 12x + 20This is a straight line with slope = 12 and the y-intercept at y = 20.The two compositions represent straight lines with a slope of 12.Because (g.f)(x) has a larger intercept, the greater production.Answer:g(f(x)) produces the greatest output.


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