math-calculus

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the absolute value function
g(x) = |5-x| can be written as a piecewise function. the piecewise function which represents g(x) is

this have to be g(x) = x-5 if x be greater to or equal to five. and the negative piece have to be 5-x. does it matter if i write -5+x instead of 5-x?

which of following is root of equation |3x-1| = -5

i get -4/3 for this.

  • math-calculus -

    from x = -oo to x = 5
    g = -5 + x

    from x = 5 to x = oo
    g = x - 5

    3x-1 = -5
    3 x = -4
    x = -4/3

  • math-calculus -

    thank you for the 3x-1 = -5 it says in back of book that there are no roots of the equation |3x-1| = -5 and i not see how that be possible.

  • math-calculus -

    By definition
    | anything | has to be a positive number or at least zero
    so |3x-1\ = -5 would contradict the very definition of absolute value,
    So without even showing a single step, we can say that there is no solution.

    if you verify your answer of -4/3, ...
    LS = |3(-4/3) - 1|
    = | -5|
    = +5
    RS = -5

    LS ≠ RS , so .... no solution

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