math
posted by SC on .
Let f(x)=x+2 Ix3I and g(x)=3x1
Find all solutions to the equation f(g(x))=4x
So this is what I did...
(3x1)+2 I(3x1)3I=4x
(3x1)+2 I3x4I=4x
This is where I got stuck. What do I do with the absolute value? and this part?(3x1)+2=3x+1 ??

Replace x3 with x3 and solve. Accept only solutions for which x>3
Then replace x3 with 3x and solve again. Accept only solutions for which x<3 
Solve it in regions:
a) when 3x>4 or x>4/3
then 3x1+6x8=4x
13x=9
x=9/13 check that. IF so, then not a solution, because x is not>4/3
b) when 3x<4 or x<4/3
then 3x16x+2=4x
x=1 which is true, because x<4/3
check my figuring. 
Thanks you! I get it now!