anonymous
  • anonymous
Given b(x)=|x+4|, what is b(-10)? A.-10 B. -6 C. 6 D. 14
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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SolomonZelman
  • SolomonZelman
at first, plug in -10 for x, into the \(|x+4|\).
anonymous
  • anonymous
-6?
SolomonZelman
  • SolomonZelman
no, hold on, when you plug in -10 for x, you get: \(\small b(x)=\left|x+4\right|\) \(\small b(\color{red}{-10})=\left|\color{red}{-10}+4\right|\) \(\small b(\color{red}{-10})=\left|-6\right|\)

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SolomonZelman
  • SolomonZelman
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)
anonymous
  • anonymous
so would it be 6 instead of negative 6?
SolomonZelman
  • SolomonZelman
|dw:1437934269242:dw|
SolomonZelman
  • SolomonZelman
So, yes the answer is 6.
SolomonZelman
  • SolomonZelman
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
SolomonZelman
  • SolomonZelman
So, lets review the work we have to do:
SolomonZelman
  • SolomonZelman
\(\small b(x)=\left|x+4\right|\) \(\small b(\color{red}{-10})=\left|\color{red}{-10}+4\right|\) \(\small b(-10)=\left|-6\right|\) \(\small b(-10)=-6\)
SolomonZelman
  • SolomonZelman
if you want to ask anything you are always welcome to do so...:)
anonymous
  • anonymous
That helps a lot! Thank you so much! Would you be able to help with another problem?
anonymous
  • anonymous
@SolomonZelman
SolomonZelman
  • SolomonZelman
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.
anonymous
  • anonymous
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
SolomonZelman
  • SolomonZelman
I will show you an example on two different functions.
SolomonZelman
  • SolomonZelman
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: \(\large\color{black}{ \displaystyle (\color{blue}{f}^\circ \color{red}{g})(x)=\color{blue}{f(~\color{red}{g(x)}~)}=3\left(\frac{5}{x}\right)^3+2 }\) \(\large\color{black}{ \displaystyle (\color{blue}{f}^\circ \color{red}{g})(x)=\color{blue}{f(~\color{red}{g(x)}~)}=3\frac{5^3}{x^3}+2 }\) \(\large\color{black}{ \displaystyle (\color{blue}{f}^\circ \color{red}{g})(x)=\color{blue}{f(~\color{red}{g(x)}~)}=3\frac{125}{x^3}+2 }\) \(\large\color{black}{ \displaystyle (\color{blue}{f}^\circ \color{red}{g})(x)=\color{blue}{f(~\color{red}{g(x)}~)}=\frac{375}{x^3}+2 }\)
SolomonZelman
  • SolomonZelman
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).
SolomonZelman
  • SolomonZelman
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.
SolomonZelman
  • SolomonZelman
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
SolomonZelman
  • SolomonZelman
now, lets find (fº g)(x) for each answer choice together: which one do you want to start from?
anonymous
  • anonymous
Which do you think would work better?
anonymous
  • anonymous
We can just start from A
SolomonZelman
  • SolomonZelman
yes, lets do that.
SolomonZelman
  • SolomonZelman
f(x) =x² g(x) = 1/x (fº g)(x) = f(g(x)) = (1/x)²=1²/x²=1/x²
SolomonZelman
  • SolomonZelman
so is A the answer or not?
anonymous
  • anonymous
no!
SolomonZelman
  • SolomonZelman
yes, it is not the answer.
SolomonZelman
  • SolomonZelman
lets do the next one, but this one i will ask you to take a shot on
SolomonZelman
  • SolomonZelman
f(x)=2/x g(x) = 2/x (fº g)(x) = ? (go ahead)
anonymous
  • anonymous
(2/x)^2 =x^2=2/x^2 is that how we set it up
SolomonZelman
  • SolomonZelman
(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)
SolomonZelman
  • SolomonZelman
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)
SolomonZelman
  • SolomonZelman
now, you need to simplify this. can you do that?
anonymous
  • anonymous
I got 1/x is that correct?
SolomonZelman
  • SolomonZelman
|dw:1437937373887:dw|
SolomonZelman
  • SolomonZelman
|dw:1437937442588:dw|
anonymous
  • anonymous
then would it just be x? plain and simple?
SolomonZelman
  • SolomonZelman
yes
SolomonZelman
  • SolomonZelman
it is =x
SolomonZelman
  • SolomonZelman
and thus B is the answer
anonymous
  • anonymous
AHA! Thank you so much

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