A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
Given b(x)=x+4, what is b(10)?
A.10
B. 6
C. 6
D. 14
anonymous
 one year ago
Given b(x)=x+4, what is b(10)? A.10 B. 6 C. 6 D. 14

This Question is Closed

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1at first, plug in 10 for x, into the \(x+4\).

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1no, hold on, when you plug in 10 for x, you get: \(\small b(x)=\leftx+4\right\) \(\small b(\color{red}{10})=\left\color{red}{10}+4\right\) \(\small b(\color{red}{10})=\left6\right\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1What 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
 one year ago
Best ResponseYou've already chosen the best response.0so would it be 6 instead of negative 6?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1dw:1437934269242:dw

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1So, yes the answer is 6.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1in other words, the distance from 0 to 6 is 6. why is it so that 06=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
 one year ago
Best ResponseYou've already chosen the best response.1So, lets review the work we have to do:

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(\small b(x)=\leftx+4\right\) \(\small b(\color{red}{10})=\left\color{red}{10}+4\right\) \(\small b(10)=\left6\right\) \(\small b(10)=6\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1if you want to ask anything you are always welcome to do so...:)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That helps a lot! Thank you so much! Would you be able to help with another problem?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Yes, 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
 one year ago
Best ResponseYou've already chosen the best response.0For 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)= x2/3 and g(x)= 23x D) f(x)=1/2x2 and g(x)= 1/2x+2

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1I will show you an example on two different functions.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1So, 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
 one year ago
Best ResponseYou've already chosen the best response.1so 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
 one year ago
Best ResponseYou've already chosen the best response.1my 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
 one year ago
Best ResponseYou've already chosen the best response.1I 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)= x2/3 and g(x)= 23x D) f(x)=1/2x2 and g(x)= 1/2x+2

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1now, lets find (fº g)(x) for each answer choice together: which one do you want to start from?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Which do you think would work better?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0We can just start from A

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1yes, lets do that.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1f(x) =x² g(x) = 1/x (fº g)(x) = f(g(x)) = (1/x)²=1²/x²=1/x²

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1so is A the answer or not?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1yes, it is not the answer.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1lets do the next one, but this one i will ask you to take a shot on

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1f(x)=2/x g(x) = 2/x (fº g)(x) = ? (go ahead)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0(2/x)^2 =x^2=2/x^2 is that how we set it up

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1(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
 one year ago
Best ResponseYou've already chosen the best response.1all 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
 one year ago
Best ResponseYou've already chosen the best response.1now, you need to simplify this. can you do that?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I got 1/x is that correct?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1dw:1437937373887:dw

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1dw:1437937442588:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0then would it just be x? plain and simple?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1and thus B is the answer

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0AHA! Thank you so much
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.