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.

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. 

for ex: the reciprocal of 3/4 is 4/3. it is the opposite.

reciprocal definition:

a mathematical expression or function so related to another that their product is one; the quantity obtained by dividing the number one by a given quantity.

step-by-step explanation: