Question

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

Answer 1

at first, plug in -10 for x, into the \(|x+4|\).

Answer 2

-6?

Answer 3

no, hold on, when you plug in -10 for x, you get:

\(\small b(x)=\left|x+4\right|\)
\(\small b(\color{red}{-10})=\left|\color{red}{-10}+4\right|\)
\(\small b(\color{red}{-10})=\left|-6\right|\)

Answer 4

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)

Answer 5

so would it be 6 instead of negative 6?

Answer 6

So, yes the answer is 6.

Answer 7

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

Answer 8

So, lets review the work we have to do:

Answer 9

\(\small b(x)=\left|x+4\right|\)
\(\small b(\color{red}{-10})=\left|\color{red}{-10}+4\right|\)
\(\small b(-10)=\left|-6\right|\)
\(\small b(-10)=-6\)

Answer 10

if you want to ask anything you are always welcome to do so...:)

Answer 11

That helps a lot! Thank you so much! Would you be able to help with another problem?

Answer 12

@SolomonZelman

Answer 13

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.

Answer 14

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

Answer 15

I will show you an example on two different functions.

Answer 16

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:

\(\large\color{black}{ \displaystyle (\color{blue}{f}^\circ \color{red}{g})(x)=\color{blue}{f(~\color{red}{g(x)}~)}=3\left(\frac{5}{x}\right)^3+2 }\)

\(\large\color{black}{ \displaystyle (\color{blue}{f}^\circ \color{red}{g})(x)=\color{blue}{f(~\color{red}{g(x)}~)}=3\frac{5^3}{x^3}+2 }\)

\(\large\color{black}{ \displaystyle (\color{blue}{f}^\circ \color{red}{g})(x)=\color{blue}{f(~\color{red}{g(x)}~)}=3\frac{125}{x^3}+2 }\)

\(\large\color{black}{ \displaystyle (\color{blue}{f}^\circ \color{red}{g})(x)=\color{blue}{f(~\color{red}{g(x)}~)}=\frac{375}{x^3}+2 }\)

Answer 17

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).

Answer 18

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.

Answer 19

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

Answer 20

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

Answer 21

Which do you think would work better?

Answer 22

We can just start from A

Answer 23

yes, lets do that.

Answer 24

f(x) =x²
g(x) = 1/x

(fº g)(x) = f(g(x)) = (1/x)²=1²/x²=1/x²

Answer 25

so is A the answer or not?

Answer 26

no!

Answer 27

yes, it is not the answer.

Answer 28

lets do the next one, but this one i will ask you to take a shot on

Answer 29

f(x)=2/x
g(x) = 2/x

(fº g)(x) = ?

(go ahead)

Answer 30

(2/x)^2 =x^2=2/x^2
is that how we set it up

Answer 31

(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)

Answer 32

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)