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Thread: Function

  1. #1
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    Function



    $\displaystyle f(x)=7$

    $\displaystyle 7=\frac{1}{2}|4x| -1 $ or $\displaystyle -7=\frac{1}{2} |4x| -1$

    I tried solving the second one but didn't get it...Please Help!!!
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Function

    $\displaystyle \dfrac{|4x|}{2}-1=7\Leftrightarrow |4x|=16\Leftrightarrow x=\pm 4$
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  3. #3
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    Re: Function

    Quote Originally Posted by theloser View Post


    $\displaystyle f(x)=7$

    $\displaystyle 7=\frac{1}{2}|4x| -1 $ or $\displaystyle -7=\frac{1}{2} |4x| -1$

    I tried solving the second one but didn't get it...Please Help!!!
    "The second one"? Do you mean $\displaystyle -7= \frac{1}{2}|4x|- 1$?
    There is no reason why you should! The problem is to solve f(x)= 7, not f(x)= -7.
    (And, in fact, since it leads to $\displaystyle \frac{1}{2}|4x|= -6$, there is no x satisfying that equation.)
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  4. #4
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    Re: Function

    $\displaystyle f(x)=|x+4|$
    $\displaystyle f(x)=20$
    $\displaystyle 20=|x+4| or -20=|x+4|$

    Then how come for this one I should switch the signs?
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  5. #5
    MHF Contributor FernandoRevilla's Avatar
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    Re: Function

    If $\displaystyle |x+4|=20$ then, $\displaystyle x+4=20$ or $\displaystyle x+4=-20$.
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  6. #6
    MHF Contributor Siron's Avatar
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    Re: Function

    In general:
    If $\displaystyle x<0$ then $\displaystyle |x|=-x$
    If $\displaystyle x>=0$ then $\displaystyle |x|=x$

    So that means:
    $\displaystyle 20=|x+4| \Leftrightarrow 20=x+4$
    or
    $\displaystyle 20=|x+4| \Leftrightarrow 20=-(x+4)$

    ...
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  7. #7
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    Re: Function

    Quote Originally Posted by Siron View Post
    In general:
    If $\displaystyle x<0$ then $\displaystyle |x|=-x$
    If $\displaystyle x>=0$ then $\displaystyle |x|=x$

    So that means:
    $\displaystyle 20=|x+4| \Leftrightarrow 20=x+4$
    or
    $\displaystyle 20=|x+4| \Leftrightarrow 20=-(x+4)$

    ...
    This really helped me understand this soo much! Thanks
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