Question

For the functions f(x) = 2x − 6 and g(x) = 5x + 1, which composition produces the greatest output?
Both compositions produce the same output.
Neither composition produces an output.
f(g(x)) produces the greatest output.
g(f(x)) produces the greatest output.
@mertsj @jim_thompson5910

Answer 1

are you able to determine f(g(x)) ?

Answer 2

I have trouble with it.

Answer 3

maybe we can write it differently like instead of f(g(x)) we can write f o g

Answer 4

and for g(f(x)) -> g o f

Answer 5

I had to read these questions from right to left when I first did them

Answer 6

to find f(g(x)), you first replace every x with g(x)

\[\Large f(x) = 2x - 6\]
\[\Large f({\color{red}{g(x)}}) = 2({\color{red}{g(x)}}) - 6\]

then on the right side, you replace g(x) with what its definition is. In this case, g(x) = 5x+1

\[\Large f({\color{red}{g(x)}}) = 2({\color{red}{5x+1}}) - 6\]

making sense?

Answer 7

Kinda, yes

Answer 8

what does 2(5x+1) - 6 simplify to?

Answer 9

or how I like to put it ... insert your entire g(x) inside the x of the f(x)

\[f(x) = 2x-6\]
\[g(x) = 5x+1\]

\[2(5x+1)-6\]
then use distribution

Answer 10

Distribute the 2 in the parenthesis?

Answer 11

yes, then what?

Answer 12

distribute the 2 for (5x+1) and then combine like terms

Answer 13

Is it possible to multiply 5x by 2?

Answer 14

yes you will multiply the outer 2 by each term inside

Answer 15

distribution is multiplication
so multiply 2 times 5x and 2 x 1