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

- anonymous

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- jim_thompson5910

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

- anonymous

I have trouble with it.

- UsukiDoll

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

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## More answers

- UsukiDoll

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

- UsukiDoll

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

- jim_thompson5910

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?

- anonymous

Kinda, yes

- jim_thompson5910

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

- UsukiDoll

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

- anonymous

Distribute the 2 in the parenthesis?

- jim_thompson5910

yes, then what?

- UsukiDoll

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

- anonymous

Is it possible to multiply 5x by 2?

- jim_thompson5910

yes you will multiply the outer 2 by each term inside

- UsukiDoll

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

- jim_thompson5910

|dw:1434845209689:dw|

- anonymous

(10x + 2)-6

- jim_thompson5910

you can toss those parenthesis since they aren't needed

- UsukiDoll

correct
10x+2-6
so now we need 2-6

- anonymous

-4

- UsukiDoll

\[2(5x+1)-6 \rightarrow 10x+2-6 \rightarrow 10x-4\]

- UsukiDoll

yes so that's our f(g(x)) or f o g
10x - 4

- anonymous

How do I translate that to the answer choices.

- UsukiDoll

now we need g(f(x)) or g o f
it means place your entire f(x) equation inside the x for g(x)
\[f(x) = 2x-6 \]
\[g(x) =5x+1\]

- jim_thompson5910

are you able to use these steps to figure out g(f(x)) ?

- anonymous

can't wait to see the answer to ", which composition produces the greatest output?"

- UsukiDoll

maybe after we have the new equation we let x = any number and whoever has the highest number has the highest output idk just guessing

- anonymous

this is like the seventh time i have seen this question
written by a mathematical illiterate
what does "produces the greatest output" mean?
it means nothing

- UsukiDoll

blame the publishers.

- anonymous

I'm really confused.

- anonymous

you ought to be !

- anonymous

How do I set up g(f(x))?

- UsukiDoll

anyway... we need g(f(x)) or g o f
which means we place our entire f(x) function into the x's of the g(x) function

- UsukiDoll

recall that our functions are f(x) = 2x-6 and g(x) = 5x+1

- anonymous

5(2x-6)+1 ?

- jim_thompson5910

Start with g(x) and replace EVERY x with f(x)
\[\Large g(x) = 5x + 1\]
\[\Large g({\color{red}{f(x)}}) = 5({\color{red}{f(x)}}) + 1\]

- jim_thompson5910

then on the right side, replace f(x) with 2x-6
so yeah you have it, 5(2x-6) + 1

- UsukiDoll

O_O unheard that's right... now we need to distribute and simplify

- jim_thompson5910

simplify 5(2x-6) + 1

- UsukiDoll

what is 5 times 2x
and what is 5 x -6 ?

- anonymous

10x+30+1

- UsukiDoll

you have a sign error

- UsukiDoll

5 multiplied by -6 = ?

- anonymous

Oops, yeah, I dont have my glasses on. One sec.

- UsukiDoll

xD it's ok.. I had trouble reading my math book last semester.. careless mistakes on my midterms.. xD

- anonymous

-30

- UsukiDoll

yes
\[10x-30+1\]

- UsukiDoll

so now what is -30+1 ?

- anonymous

-29

- UsukiDoll

mhm \[10x-29\] is our g(f(x))
and \[10x-4 \] is our f(g(x))

- anonymous

So how does that translate to my answer choices.

- anonymous

Which is more?

- jim_thompson5910

Let's say x = 0.
What is f(g(x)) equal to?
What is g(f(x)) equal to?

- anonymous

10x-4
10x+-29

- jim_thompson5910

in each case, replace x with 0 and compute

- UsukiDoll

subsitute x = 0 into both equations

- anonymous

0-4
0+-29

- UsukiDoll

ok so what's 0-4 and 0-29?

- anonymous

4
29

- UsukiDoll

uhhhhh... no... that's positive numbers... we are dealing with negative numbers

- UsukiDoll

think of it as ... you are charged $4 but don't have any money ... you have a negative balance

- anonymous

-4
-29

- UsukiDoll

yes
:)

- UsukiDoll

now... bigger negative numbers are much smaller in value than single digit negative numbers

- anonymous

so, f(g(x))!!

- UsukiDoll

yeah... -4 is bigger than -29

- anonymous

Thank you.

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