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anonymous
 one year ago
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
 one year ago
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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jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2are you able to determine f(g(x)) ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I have trouble with it.

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1maybe we can write it differently like instead of f(g(x)) we can write f o g

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1and for g(f(x)) > g o f

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1I had to read these questions from right to left when I first did them

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2to 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?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2what does 2(5x+1)  6 simplify to?

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1or how I like to put it ... insert your entire g(x) inside the x of the f(x) \[f(x) = 2x6\] \[g(x) = 5x+1\] \[2(5x+1)6\] then use distribution

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Distribute the 2 in the parenthesis?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2yes, then what?

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1distribute the 2 for (5x+1) and then combine like terms

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Is it possible to multiply 5x by 2?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2yes you will multiply the outer 2 by each term inside

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1distribution is multiplication so multiply 2 times 5x and 2 x 1

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2dw:1434845209689:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2you can toss those parenthesis since they aren't needed

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1correct 10x+26 so now we need 26

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1\[2(5x+1)6 \rightarrow 10x+26 \rightarrow 10x4\]

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1yes so that's our f(g(x)) or f o g 10x  4

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0How do I translate that to the answer choices.

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1now we need g(f(x)) or g o f it means place your entire f(x) equation inside the x for g(x) \[f(x) = 2x6 \] \[g(x) =5x+1\]

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2are you able to use these steps to figure out g(f(x)) ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0can't wait to see the answer to ", which composition produces the greatest output?"

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1maybe 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
 one year ago
Best ResponseYou've already chosen the best response.0this 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
 one year ago
Best ResponseYou've already chosen the best response.1blame the publishers.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm really confused.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0How do I set up g(f(x))?

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1anyway... 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
 one year ago
Best ResponseYou've already chosen the best response.1recall that our functions are f(x) = 2x6 and g(x) = 5x+1

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2Start 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
 one year ago
Best ResponseYou've already chosen the best response.2then on the right side, replace f(x) with 2x6 so yeah you have it, 5(2x6) + 1

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1O_O unheard that's right... now we need to distribute and simplify

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2simplify 5(2x6) + 1

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1what is 5 times 2x and what is 5 x 6 ?

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1you have a sign error

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.15 multiplied by 6 = ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oops, yeah, I dont have my glasses on. One sec.

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1xD it's ok.. I had trouble reading my math book last semester.. careless mistakes on my midterms.. xD

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1so now what is 30+1 ?

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1mhm \[10x29\] is our g(f(x)) and \[10x4 \] is our f(g(x))

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So how does that translate to my answer choices.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2Let's say x = 0. What is f(g(x)) equal to? What is g(f(x)) equal to?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2in each case, replace x with 0 and compute

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1subsitute x = 0 into both equations

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1ok so what's 04 and 029?

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1uhhhhh... no... that's positive numbers... we are dealing with negative numbers

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1think of it as ... you are charged $4 but don't have any money ... you have a negative balance

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1now... bigger negative numbers are much smaller in value than single digit negative numbers

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1yeah... 4 is bigger than 29
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