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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.

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  1. SolomonZelman
    • one year ago
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    \(\large\color{blue}{ \displaystyle f(x)=2x+3 }\) \(\large\color{red}{ \displaystyle g(x)=6x+2 }\) \(\large\color{blue}{ \displaystyle f(\color{red}{g(x)})=2\left( \color{red}{6x+2}\right)+3 =? }\)\ \(\large\color{red}{ \displaystyle g(\color{blue}{f(x)})=6\left( \color{blue}{2x+3}\right)+2 =? }\)

  2. SolomonZelman
    • one year ago
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    I 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))....

  3. SolomonZelman
    • one year ago
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    this migh be confusing, say so if it is.

  4. Agl202
    • one year ago
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    What do I do next?

  5. SolomonZelman
    • one year ago
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    evaluate each composition

  6. Agl202
    • one year ago
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    how do i do that?

  7. SolomonZelman
    • one year ago
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    expand the parenthesis in: \(\large\color{blue}{ \displaystyle f(\color{red}{g(x)})=2\left( \color{red}{6x+2}\right)+3 }\)

  8. SolomonZelman
    • one year ago
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    then simplify as much as you can (by adding like terms)

  9. Agl202
    • one year ago
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    how do I find x?

  10. SolomonZelman
    • one year ago
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    you don't need to

  11. SolomonZelman
    • one year ago
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    just simplify the f(g(x)) and g(f(x)) as much as you can

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

  13. Agl202
    • one year ago
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    f(g(x))= 19 g(f(x))= 32 right?

  14. Agl202
    • one year ago
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    So, D. is the correct choice?

  15. SolomonZelman
    • one year ago
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    f(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?

  16. SolomonZelman
    • one year ago
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    But 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.)

  17. Agl202
    • one year ago
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    no I didn't.

  18. SolomonZelman
    • one year ago
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    how did you get 19 and 32 then?

  19. Agl202
    • one year ago
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    I dunno, how did u get the 4 this equation? --> f(g(x)) = 2(6x+2)+3 = 12x+4+3 = 12x + 7

  20. SolomonZelman
    • one year ago
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    I expanded, because: |dw:1441674897461:dw|

  21. SolomonZelman
    • one year ago
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    can you see the picture fully?

  22. Agl202
    • one year ago
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    Oh... K makes sense.

  23. SolomonZelman
    • one year ago
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    yes, and same technique I applied when expanded the parenthesis in: `g(f(x))=6(2x+3)+2`

  24. SolomonZelman
    • one year ago
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    So 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) ?

  25. Agl202
    • one year ago
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    Yes, makes sense.

  26. SolomonZelman
    • one year ago
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    Ok, and as you can notice, g(f(x)) is a shift 13 units up from f(g(x)). Right?

  27. Agl202
    • one year ago
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    yes

  28. SolomonZelman
    • one year ago
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    And thus, g(f(x)) is going to be 13 {units} greater than f(g(x)), FOR ANY VALUE OF x.

  29. SolomonZelman
    • one year ago
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    And this is why choice D is right.

  30. Agl202
    • one year ago
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    Oh, I now understand. Thx for the help and understanding! :D Last year geometry was great, but Algebra 2 is a little challenge this year

  31. SolomonZelman
    • one year ago
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    Oh, you will get it:)

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