Question

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

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

Answer 1

f(g(x)) = 2 (6x + 2) + 3 = 12x + 7

for x = 1;

f(g(x)) = f(g(1)) = 12 (1) + 7 = 19

g(f(x)) = 6 (2x + 3 ) + 2 = 12x + 20

g(f(x)) = g(f(1)) = 12 (1) + 20 = 32

Thus option “D” is correct.