Posted by **SC** on Tuesday, December 8, 2009 at 9:11pm.

Let f(x)=x+2 Ix-3I and g(x)=3x-1

Find all solutions to the equation f(g(x))=-4x

So this is what I did...

(3x-1)+2 I(3x-1)-3I=-4x

(3x-1)+2 I3x-4I=-4x

This is where I got stuck. What do I do with the absolute value? and this part?(3x-1)+2=3x+1 ??

- mathh -
**drwls**, Tuesday, December 8, 2009 at 9:18pm
Replace |x-3| with x-3 and solve. Accept only solutions for which x>3

Then replace |x-3| with 3-x and solve again. Accept only solutions for which x<3

- mathh -
**bobpursley**, Tuesday, December 8, 2009 at 9:22pm
Solve it in regions:

a) when 3x>4 or x>4/3

then 3x-1+6x-8=-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 3x-1-6x+2=-4x

x=1 which is true, because x<4/3

check my figuring.

- mathh -
**SC**, Tuesday, December 8, 2009 at 9:25pm
Thanks you! I get it now!

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