does anyone know how to solve problems with composition???

Question

e.mccormick · Answer

Composition means to put one into the other.  So that is literally what you do.

anonymous · Answer

I KNOW BUT IVE FAILED THE TEST 16 TIMES ALREADY

e.mccormick · Answer

Well, what are you doing when you compose things?

anonymous · Answer

I NEED HELP

anonymous · Answer

HAVE YOU HEARD ABOUT APEXVS

anonymous · Answer

IM RETAKING MY SEMESTER 1 ALGEBRA TWO CLASS AND IT DOESNT EXPLAIN YOU RIGHT

e.mccormick · Answer

Well, the basics are this: $(f\circ g)(x)$ means the same thing as $f(g(x))$.  However, it can be a little clearer if you use different things than just ( ) to enclose things, so say $f[g(x)]$.

e.mccormick · Answer

So lets say I have $f(x)=2x+5$ and I say $g(x)=4x^2$  If I do $(f\circ g)(x)$ I can restate that as $f[g(x)]$  So, I am putting $g(x)$ inside [ ].

anonymous · Answer

UR PUTTING 4^2

e.mccormick · Answer

$g(x)=4x^2$ in brackets is $[g(x)]=[4x^2]$  So.  Let me take that $[4x^2]$ and put it inside f.  $f([4x^2])$.

e.mccormick · Answer

Well now I need to take that $f(x)=2x+5$ and replace the x in it with that [ ] statement.  

$f(x)=2x+5\implies f([4x^2])=2[4x^2]+5$

e.mccormick · Answer

Now it is an order of operations problem.  I have to simplify according to the order of operations.  ( ) or [ ] is first.  But what is inside mine is not able to be simplified, so that is OK.  Next I need to distribute the 2.  
Well now I need to take that $f(x)=2x+5$ and replace the x in it with that [ ] statement.  

$8x^2+5$

For that one, that is it.

e.mccormick · Answer

If I do it the other way, it takes a little more work.

 $(g\circ f)(x)\implies g([f(x)])$

$ f(x)=2x+5 \implies   [f(x)]=[2x+5]$

$g(x)=4x^2$ 

Put those together and  get:

$g([2x+5])=4[2x+5]^2$

anonymous · Answer

WOW THAT ALOT HARDER THAN WHAT IM DOING

e.mccormick · Answer

Now it is an order of operations again.  The power of the [ ] has to be first.  So I have to FOIL that.

$4[2x+5]^2\implies 4[(2x+5)(2x+5)]$

$4[(2x+5)(2x+5)] \implies 4[4x^2+20x+25]$

Then distribute the 4.

$4[4x^2+20x+25] \implies 16x^2+80x+100$

e.mccormick · Answer

Well, squares make it a bit harder.  You usually start these with simple variables, then move up to squares.  So I wanted to show you one that was easy one way, but harder the other.

anonymous · Answer

OKAY

anonymous · Answer

well im going to post some problems that i dont get at all can you help me???

e.mccormick · Answer

If you show me whjat you are doing with them, I can tell you where you are making mistaks.  Then you can know what you need to be more careful of and get things right!

anonymous · Answer

okay bro