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Agl202
 one year ago
Quick Help:
For the functions f(x) = 2x + 3 and g(x) = 6x + 2, which composition produces the greatest output?
Neither composition produces an output.
Both compositions produce the same output.
f(g(x)) produces the greatest output.
g(f(x)) produces the greatest output.
Agl202
 one year ago
Quick Help: For the functions f(x) = 2x + 3 and g(x) = 6x + 2, which composition produces the greatest output? Neither composition produces an output. Both compositions produce the same output. f(g(x)) produces the greatest output. g(f(x)) produces the greatest output.

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SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3\(\large\color{blue}{ \displaystyle f(x)=2x+3 }\) \(\large\color{red}{ \displaystyle g(x)=6x+2 }\) \(\large\color{blue}{ \displaystyle f(\color{red}{g(x)})=2\left( \color{red}{6x+2}\right)+3 =? }\)\ \(\large\color{red}{ \displaystyle g(\color{blue}{f(x)})=6\left( \color{blue}{2x+3}\right)+2 =? }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3I coloered each function in its color, and here belower f(x) and g(x), I am showing how to set up the f(g(x)) and g(f(x))....

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3this migh be confusing, say so if it is.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3evaluate each composition

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3expand the parenthesis in: \(\large\color{blue}{ \displaystyle f(\color{red}{g(x)})=2\left( \color{red}{6x+2}\right)+3 }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3then simplify as much as you can (by adding like terms)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3you don't need to

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3just simplify the f(g(x)) and g(f(x)) as much as you can

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3Again, posting them so that you won't need to scrol way back \(\large\color{blue}{ \displaystyle f(\color{red}{g(x)})=2\left( \color{red}{6x+2}\right)+3 =? }\)\ \(\large\color{red}{ \displaystyle g(\color{blue}{f(x)})=6\left( \color{blue}{2x+3}\right)+2 =? }\)

Agl202
 one year ago
Best ResponseYou've already chosen the best response.6f(g(x))= 19 g(f(x))= 32 right?

Agl202
 one year ago
Best ResponseYou've already chosen the best response.6So, D. is the correct choice?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3f(g(x)) = 2(6x+2)+3 = 12x+4+3 = 12x + 7  g(f(x)) = 6(2x+3)+2=12x+18+2=12x+20 did you plug in 1 for x after that?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3But you didn't have that x=1 for that, did you? (Not that it matters..... g(f(x)) is shifted 13 units up from f(g(x)), and for any x it is thus g(f(x)) is greater by 13 units.)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3how did you get 19 and 32 then?

Agl202
 one year ago
Best ResponseYou've already chosen the best response.6I dunno, how did u get the 4 this equation? > f(g(x)) = 2(6x+2)+3 = 12x+4+3 = 12x + 7

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3I expanded, because: dw:1441674897461:dw

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3can you see the picture fully?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3yes, and same technique I applied when expanded the parenthesis in: `g(f(x))=6(2x+3)+2`

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3So see how I got: `f(g(x)) = 2(6x+2)+3 = 12x+4+3 = 12x + 7` `g(f(x)) = 6(2x+3)+2=12x+18+2=12x+20` Yes (understand) / No (don't uderstand) ?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3Ok, and as you can notice, g(f(x)) is a shift 13 units up from f(g(x)). Right?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3And thus, g(f(x)) is going to be 13 {units} greater than f(g(x)), FOR ANY VALUE OF x.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3And this is why choice D is right.

Agl202
 one year ago
Best ResponseYou've already chosen the best response.6Oh, I now understand. Thx for the help and understanding! :D Last year geometry was great, but Algebra 2 is a little challenge this year

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3Oh, you will get it:)
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