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anonymous

  • one year ago

Given b(x)=|x+4|, what is b(-10)? A.-10 B. -6 C. 6 D. 14

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  1. SolomonZelman
    • one year ago
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    at first, plug in -10 for x, into the \(|x+4|\).

  2. anonymous
    • one year ago
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    -6?

  3. SolomonZelman
    • one year ago
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    no, hold on, when you plug in -10 for x, you get: \(\small b(x)=\left|x+4\right|\) \(\small b(\color{red}{-10})=\left|\color{red}{-10}+4\right|\) \(\small b(\color{red}{-10})=\left|-6\right|\)

  4. SolomonZelman
    • one year ago
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    What does "absolute value of a", written as "|a|" mean? Roughly speaking, you can define |a| as a distance from 0 to a (how much do you have to walk from a to 0)

  5. anonymous
    • one year ago
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    so would it be 6 instead of negative 6?

  6. SolomonZelman
    • one year ago
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    |dw:1437934269242:dw|

  7. SolomonZelman
    • one year ago
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    So, yes the answer is 6.

  8. SolomonZelman
    • one year ago
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    in other words, the distance from 0 to -6 is 6. why is it so that 0-6=-6 (not just 6) because the minus by 6 indicates the direction (that it is going to the left - if you look at the number line), but absolute value of -6, or |-6| is 6

  9. SolomonZelman
    • one year ago
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    So, lets review the work we have to do:

  10. SolomonZelman
    • one year ago
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    \(\small b(x)=\left|x+4\right|\) \(\small b(\color{red}{-10})=\left|\color{red}{-10}+4\right|\) \(\small b(-10)=\left|-6\right|\) \(\small b(-10)=-6\)

  11. SolomonZelman
    • one year ago
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    if you want to ask anything you are always welcome to do so...:)

  12. anonymous
    • one year ago
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    That helps a lot! Thank you so much! Would you be able to help with another problem?

  13. anonymous
    • one year ago
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    @SolomonZelman

  14. SolomonZelman
    • one year ago
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    Yes, perhaps, but I am helping another student currently. I personally don't care tho', if you post it in this thread or another one, so you can keep this post.

  15. anonymous
    • one year ago
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    For which pair of functions is (f ° g)(x) =x? A) f(x) =x^2 and g(x) = 1/x B) f(x)=2/x and g(x) = 2/x C) f(x)= x-2/3 and g(x)= 2-3x D) f(x)=1/2x-2 and g(x)= 1/2x+2

  16. SolomonZelman
    • one year ago
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    I will show you an example on two different functions.

  17. SolomonZelman
    • one year ago
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    So, lets say my function f(x) and g(x) are the following: \(\large\color{blue}{ \displaystyle f(x)=3x^3+2 \\[0.5em]}\) \(\large\color{red}{ \displaystyle g(x)=\frac{5}{x} }\) -------------------------------------------- A notation of: \((\color{blue}{f}^\circ \color{red}{g})(x)\) means the same as \(\color{blue}{f(~\color{red}{g(x)}~)}\) in other words, you take a function g(x), and plug it instead of x, into the f(x). -------------------------------------------- How would it actually go overhere? \(\large\color{black}{ \displaystyle (\color{blue}{f}^\circ \color{red}{g})(x)=\color{blue}{f(~\color{red}{g(x)}~)}=\color{blue}{3\left(\color{red}{\frac{5}{x}}\right)^3+2} }\) see how I am plugging the g(x) instead of x, into f(x)? now, we will simplify that: \(\large\color{black}{ \displaystyle (\color{blue}{f}^\circ \color{red}{g})(x)=\color{blue}{f(~\color{red}{g(x)}~)}=3\left(\frac{5}{x}\right)^3+2 }\) \(\large\color{black}{ \displaystyle (\color{blue}{f}^\circ \color{red}{g})(x)=\color{blue}{f(~\color{red}{g(x)}~)}=3\frac{5^3}{x^3}+2 }\) \(\large\color{black}{ \displaystyle (\color{blue}{f}^\circ \color{red}{g})(x)=\color{blue}{f(~\color{red}{g(x)}~)}=3\frac{125}{x^3}+2 }\) \(\large\color{black}{ \displaystyle (\color{blue}{f}^\circ \color{red}{g})(x)=\color{blue}{f(~\color{red}{g(x)}~)}=\frac{375}{x^3}+2 }\)

  18. SolomonZelman
    • one year ago
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    so all you are doing for (fº g)(x), is that you plug in the function g(x) instead of x --> into the f(x).

  19. SolomonZelman
    • one year ago
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    my function is more rather complicated, but all you need to do is to find this (fº g)(x), and which ever of the options will give you a result/answer of x, that is your answer.

  20. SolomonZelman
    • one year ago
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    I will respot the question: ---------------------- For which pair of functions is (f ° g)(x) =x? A) f(x) =x^2 and g(x) = 1/x B) f(x)=2/x and g(x) = 2/x C) f(x)= x-2/3 and g(x)= 2-3x D) f(x)=1/2x-2 and g(x)= 1/2x+2

  21. SolomonZelman
    • one year ago
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    now, lets find (fº g)(x) for each answer choice together: which one do you want to start from?

  22. anonymous
    • one year ago
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    Which do you think would work better?

  23. anonymous
    • one year ago
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    We can just start from A

  24. SolomonZelman
    • one year ago
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    yes, lets do that.

  25. SolomonZelman
    • one year ago
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    f(x) =x² g(x) = 1/x (fº g)(x) = f(g(x)) = (1/x)²=1²/x²=1/x²

  26. SolomonZelman
    • one year ago
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    so is A the answer or not?

  27. anonymous
    • one year ago
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    no!

  28. SolomonZelman
    • one year ago
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    yes, it is not the answer.

  29. SolomonZelman
    • one year ago
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    lets do the next one, but this one i will ask you to take a shot on

  30. SolomonZelman
    • one year ago
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    f(x)=2/x g(x) = 2/x (fº g)(x) = ? (go ahead)

  31. anonymous
    • one year ago
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    (2/x)^2 =x^2=2/x^2 is that how we set it up

  32. SolomonZelman
    • one year ago
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    (fº g)(x) is same as f(g(x)) so you just plug in the g(x) (in this case, 2/x), instead of x, into the f(x). so f(x) = 2/x (fº g)(x) = f(g(x))=2/(2/x)

  33. SolomonZelman
    • one year ago
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    all we did is that we took the x in f(x), and replaced it by the function g(x). (i.e. replaced the x in the function f(x), but 2/x)

  34. SolomonZelman
    • one year ago
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    now, you need to simplify this. can you do that?

  35. anonymous
    • one year ago
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    I got 1/x is that correct?

  36. SolomonZelman
    • one year ago
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    |dw:1437937373887:dw|

  37. SolomonZelman
    • one year ago
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    |dw:1437937442588:dw|

  38. anonymous
    • one year ago
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    then would it just be x? plain and simple?

  39. SolomonZelman
    • one year ago
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    yes

  40. SolomonZelman
    • one year ago
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    it is =x

  41. SolomonZelman
    • one year ago
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    and thus B is the answer

  42. anonymous
    • one year ago
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    AHA! Thank you so much

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