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math

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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 ??

  • math -

    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

  • math -

    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.

  • math -

    Thanks you! I get it now!

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