Question

For the functions f(x) = 5x − 3 and g(x) = x + 4, which composition produces the greatest output?

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

Answer 1

A. f(g(x)) basically all you are going to do is replace all the x's in f(x) with x+4
f(x+4) = 5(x+4) - 3
Now solve...
Distribute
= 5x + 20 - 3
= 5x + 17
B. Now do the opposite of A.
g(5x-3) = 5x-3 + 4
= 5x + 1

C. Wrong. They don't give out the same output.

D. I think it's this one since there isn't a real answer

Answer 2

A. f(g(x)) produces the greatest output