1. Composite Function question

Hi,
I'm a little confused over one of the questions I've been given for composite functions. I have the answer but I can't see how exactly we got there.
The function given is q(p(x))

Using for p:x=8/2x
q:x=3x.

So the solution given is 3(8/2x) = 24/2x = 12/x

Question
When we multiply 8/2x by the function of q which is 3x, why do we only mulitply the top line and not the bottom? I tried to do it 3(8/2x) = 24/6x = 12/3x = 4/x which is obviously incorrect.

Thanks

2. Re: Composite Function question

Hi Davein,

actually we do multiply the bottom by 1.

3(8/2x) = (3/1) (8/2x) ; 3/1=3

(3*8) / (1*2x) = 24/2x = 12/x

p/s:
a(x-y)=ax-ay
a(x+y)=ax+ay
a(xy)=axy
a(x/y)=ax/y
(x/y)^2=x^2/y^2

cheers.......

3. Re: Composite Function question

Hi,
Thanks for the reply. I obviously didn't learn rule 4 below. Thanks.
a(x-y)=ax-ay
a(x+y)=ax+ay
a(xy)=axy
a(x/y)=ax/y
(x/y)^2=x^2/y^2