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

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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

Mathematics
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are you able to determine f(g(x)) ?
I have trouble with it.
maybe we can write it differently like instead of f(g(x)) we can write f o g

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and for g(f(x)) -> g o f
I had to read these questions from right to left when I first did them
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?
Kinda, yes
what does 2(5x+1) - 6 simplify to?
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
Distribute the 2 in the parenthesis?
yes, then what?
distribute the 2 for (5x+1) and then combine like terms
Is it possible to multiply 5x by 2?
yes you will multiply the outer 2 by each term inside
distribution is multiplication so multiply 2 times 5x and 2 x 1
|dw:1434845209689:dw|
(10x + 2)-6
you can toss those parenthesis since they aren't needed
correct 10x+2-6 so now we need 2-6
-4
\[2(5x+1)-6 \rightarrow 10x+2-6 \rightarrow 10x-4\]
yes so that's our f(g(x)) or f o g 10x - 4
How do I translate that to the answer choices.
now we need g(f(x)) or g o f it means place your entire f(x) equation inside the x for g(x) \[f(x) = 2x-6 \] \[g(x) =5x+1\]
are you able to use these steps to figure out g(f(x)) ?
can't wait to see the answer to ", which composition produces the greatest output?"
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
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
blame the publishers.
I'm really confused.
you ought to be !
How do I set up g(f(x))?
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
recall that our functions are f(x) = 2x-6 and g(x) = 5x+1
5(2x-6)+1 ?
Start with g(x) and replace EVERY x with f(x) \[\Large g(x) = 5x + 1\] \[\Large g({\color{red}{f(x)}}) = 5({\color{red}{f(x)}}) + 1\]
then on the right side, replace f(x) with 2x-6 so yeah you have it, 5(2x-6) + 1
O_O unheard that's right... now we need to distribute and simplify
simplify 5(2x-6) + 1
what is 5 times 2x and what is 5 x -6 ?
10x+30+1
you have a sign error
5 multiplied by -6 = ?
Oops, yeah, I dont have my glasses on. One sec.
xD it's ok.. I had trouble reading my math book last semester.. careless mistakes on my midterms.. xD
-30
yes \[10x-30+1\]
so now what is -30+1 ?
-29
mhm \[10x-29\] is our g(f(x)) and \[10x-4 \] is our f(g(x))
So how does that translate to my answer choices.
Which is more?
Let's say x = 0. What is f(g(x)) equal to? What is g(f(x)) equal to?
10x-4 10x+-29
in each case, replace x with 0 and compute
subsitute x = 0 into both equations
0-4 0+-29
ok so what's 0-4 and 0-29?
4 29
uhhhhh... no... that's positive numbers... we are dealing with negative numbers
think of it as ... you are charged $4 but don't have any money ... you have a negative balance
-4 -29
yes :)
now... bigger negative numbers are much smaller in value than single digit negative numbers
so, f(g(x))!!
yeah... -4 is bigger than -29
Thank you.

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