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    I somewhat have trouble with getting all indices on one side
    so the question is

    3/4x to the power of 3 - 6/x = 0

    So i took the 6/x to the other side, but now with the powers wouldnt I take the 6/x and multiply x3 by the x on that side to get x4? the answer book gets x down to the power of 3 but I dont know how
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    Can you use brackets to make it clear what you mean 3/4x^3 could mean quite a few things.
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    (Original post by SunDun111)
    ...
    As above, could you provide a picture or make use of brackets to clarify your meaning. What you've written could mean \left(\frac{3}{4x}\right)^3, it could mean 3/4 \cdot x^3 it could mean \frac{3}{4x^3}, etc...
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    (Original post by Zacken)
    As above, could you provide a picture or make use of brackets to clarify your meaning. What you've written could mean \left(\frac{3}{4x}\right)^3, it could mean 3/4 \cdot x^3 it could mean \frac{3}{4x^3}, etc...
    Its 3/4 as a number then x3 next to it, basically 0.75x to the power of 3
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    (Original post by SunDun111)
    Its 3/4 as a number then x3 next to it, basically 0.75x to the power of 3
    Okay, so \frac{3x^3}{4} - \frac{6}{x} = 0. First step, as you said, bring the 6/x to the other side, this gets us: \frac{3x^3}{4} = \frac{6}{x}.

    Multiply both sides by x:

    \displaystyle 

\begin{equation*}\frac{3x^4}{4} = 6\end{equation*}.

    Divide both sides by \frac{3}{4}:

    \displaystyle 

\begin{equation*}x^4 = 6 \times \frac{4}{3} = 8\end{equation*}.

    Take the fourth root of both sides, see if you can do this yourself:
    Spoiler:
    Show
    x = \sqrt[4]{8}


    Which step don't you understand?
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    (Original post by Zacken)
    Okay, so \frac{3x^3}{4} - \frac{6}{x} = 0. First step, as you said, bring the 6/x to the other side, this gets us: \frac{3x^3}{4} = \frac{6}{x}.

    Multiply both sides by x:

    \displaystyle 

\begin{equation*}\frac{3x^4}{4} = 6\end{equation*}.

    Divide both sides by \frac{3}{4}:

    \displaystyle 

\begin{equation*}x^4 = 6 \times \frac{4}{3} = 8\end{equation*}.

    Take the fourth root of both sides, see if you can do this yourself:
    Spoiler:
    Show
    x = \sqrt[4]{8}

    Which step don't you understand?
    Nothing thanks, I knew how to do it and I got what you got but I realised I wasnt getting the right answer because i copied down the wrong equation
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    (Original post by SunDun111)
    Nothing thanks, I knew how to do it and I got what you got but I realised I wasnt getting the right answer because i copied down the wrong equation
    Ouch, that's good then - you know your understanding and methodology is correct. Well done!
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    (Original post by Zacken)
    Ouch, that's good then - you know your understanding and methodology is correct. Well done!
    Thanks, quick question when you differentiate something and asked to prove its a decreasing function what do you do?
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    (Original post by SunDun111)
    Thanks, quick question when you differentiate something and asked to prove its a decreasing function what do you do?
    Remember yesterday I told you that to show a function is increasing, you show it's derivative is always positive? Can you guess what you have to do for decreasing functions?
    Spoiler:
    Show
    Show the derivative is always negative. (i.e: always less than 0).
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    (Original post by Zacken)
    Remember yesterday I told you that to show a function is increasing, you show it's derivative is always positive? Can you guess what you have to do for decreasing functions?
    Spoiler:
    Show
    Show the derivative is always negative. (i.e: always less than 0).
    too much revision I forget things haha thanks
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    (Original post by SunDun111)
    too much revision I forget things haha thanks
    Don't worry about it, it's good that you're asking and clearing things up. You're welcome.
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    (Original post by Zacken)
    Don't worry about it, it's good that you're asking and clearing things up. You're welcome.
    I looks at your posts on Domains and Range's and for some reason I simply struggle to understand it, I really need to learn it as in C3 a lot of topics are linked with it, do you recommend any good videos about it? because i really struggle with it
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    (Original post by SunDun111)
    I looks at your posts on Domains and Range's and for some reason I simply struggle to understand it, I really need to learn it as in C3 a lot of topics are linked with it, do you recommend any good videos about it? because i really struggle with it
    Which bits do you struggle to understand?

    If I told you to find me the domain of \frac{1}{x-1} what is your thought process?
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    (Original post by Zacken)
    Which bits do you struggle to understand?

    If I told you to find me the domain of \frac{1}{x-1} what is your thought process?
    I struggle with all of it, in the exercise book the questions are difficult because they ask me to sketch the graph of it which I hate doing because some of the graphs are difficult to draw,
    Is it the number for which the calculator displays an error?
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    (Original post by SunDun111)
    I struggle with all of it, in the exercise book the questions are difficult because they ask me to sketch the graph of it which I hate doing because some of the graphs are difficult to draw,
    Is it the number for which the calculator displays an error?
    Yes, whenever you're given a fraction function (called a rational function), the domain will be the set of numbers for which the denominator is not zero.

    So in this case, the domain is x- 1 \neq 0 \iff x \neq 1.

    What about the domain of \sqrt{x-2}? What do you know about square roots, what does that mean for their domain?

    Get used to graph sketching, it's a very important skill.
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    (Original post by Zacken)
    Yes, whenever you're given a fraction function (called a rational function), the domain will be the set of numbers for which the denominator is not zero.

    So in this case, the domain is x- 1 \neq 0 \iff x \neq 1.

    What about the domain of \sqrt{x-2}? What do you know about square roots, what does that mean for their domain?

    Get used to graph sketching, it's a very important skill.
    Would it be 1 because 1-2 is negative square root?
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    (Original post by SunDun111)
    Would it be 1 because 1-2 is negative square root?
    No, in this case you know that your square root is valid as long as the inside of it is positive or zero, so x-2 \geq 0 \iff x \geq 2.

    So your domain is x \geq 2. Perhaps you should go over this with a teacher?
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    (Original post by Zacken)
    No, in this case you know that your square root is valid as long as the inside of it is positive or zero, so x-2 \geq 0 \iff x \geq 2.

    So your domain is x \geq 2. Perhaps you should go over this with a teacher?
    Yeah I'm going to when I'm back at school on the 11th, but its so long I want to learn it now, just looking for a few videos.
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    (Original post by SunDun111)
    Yeah I'm going to when I'm back at school on the 11th, but its so long I want to learn it now, just looking for a few videos.
    Video 1

    Video 2
 
 
 
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