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    I can't seem to figure out where I'm going wrong.

    Y= f(1/3 multiplied by x)
    Then I'm given f(x) = x^3

    I put x into the function and get x^3/3 but I'm told it should be x^3/27

    Where am I going wrong.
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    (Original post by Chrollo-Lucilfer)
    I can't seem to figure out where I'm going wrong.

    Y= f(1/3 multiplied by x)
    Then I'm given f(x) = x^3

    I put x into the function and get x^3/3 but I'm told it should be x^3/27

    Where am I going wrong.
    If \displaystyle f(x)=x^3

    then

    \displaystyle f\left(\frac{1}{3}x\right) = \left(\frac{1}{3}x\right)^3

    Can you see why this is equal to \frac{x^3}{27} and not \frac{x^3}{3} ?
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    (Original post by notnek)
    If \displaystyle f(x)=x^3

    then

    \displaystyle f\left(\frac{1}{3}x\right) = \left(\frac{1}{3}x\right)^3

    Can you see why this is equal to \frac{x^3}{27} and not \frac{x^3}{3} ?
    Thanks. Can you just tell me where I go wrong on this question:

    y=f(1/3 multiplied by x)
    F(x) = 1/x

    So I write:
    1 divided by 1/3 multiplied by x
    If I follow BIDMAS I get 1 x 3/1 x X
    Leading to 3x

    But I know the correct answer to be 3/x

    So I'm curious why it's written 1/3 x X instead of just x/3?
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    (Original post by Chrollo-Lucilfer)
    Thanks. Can you just tell me where I go wrong on this question:

    y=f(1/3 multiplied by x)
    F(x) = 1/x

    So I write:
    1 divided by 1/3 multiplied by x
    If I follow BIDMAS I get 1 x 3/1 x X
    Leading to 3x

    But I know the correct answer to be 3/x

    So I'm curious why it's written 1/3 x X instead of just x/3?
    Just follow what Notnek did above such that x \mapsto \frac{1}{3}x

    So if \displaystyle f(x)=\frac{1}{x}

    then \displaystyle f(\frac{1}{3}x)=\frac{1}{\frac{1  }{3}x}

    then multiply top and bottom of the main fraction by 3

    P.S. It doesn't matter whether it is written as \frac{1}{3}x or \frac{x}{3} as they mean the exact same thing.
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    (Original post by Chrollo-Lucilfer)
    Thanks. Can you just tell me where I go wrong on this question:

    y=f(1/3 multiplied by x)
    F(x) = 1/x

    So I write:
    1 divided by 1/3 multiplied by x
    If I follow BIDMAS I get 1 x 3/1 x X
    Leading to 3x

    But I know the correct answer to be 3/x

    So I'm curious why it's written 1/3 x X instead of just x/3?
    I'm not sure what you mean when you say you are following BIDMAS here.

    For \displaystyle \frac{1}{\left(\frac{1}{3} x \right) }, you could multiply top and bottom of the fraction by 3:

    \displaystyle \frac{1}{\left(\frac{1}{3} x \right) } = \frac{1 \times 3}{\left(\frac{1}{3}x\times 3\right)}=\frac{3}{x}

    Alternatively, you could split up the fraction (reverse multiplication of fractions):

    \displaystyle \frac{1}{\left(\frac{1}{3} x \right) } = \frac{1}{\left(\frac{1}{3} \right)}\times \frac{1}{x} = 3 \times \frac{1}{x} = \frac{3}{x}
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    (Original post by notnek)
    I'm not sure what you mean when you say you are following BIDMAS here.

    For \displaystyle \frac{1}{\left(\frac{1}{3} x \right) }, you could multiply top and bottom of the fraction by 3:

    \displaystyle \frac{1}{\left(\frac{1}{3} x \right) } = \frac{1 \times 3}{\left(\frac{1}{3}x\times 3\right)}=\frac{3}{x}

    Alternatively, you could split up the fraction (reverse multiplication of fractions):

    \displaystyle \frac{1}{\left(\frac{1}{3} x \right) } = \frac{1}{\left(\frac{1}{3} \right)}\times \frac{1}{x} = 3 \times \frac{1}{x} = \frac{3}{x}
    I interpreted it as 1 divided by 1/3 multiplied by x. If I multiply 1/3 and x I get. x/3 then dividing with one I get 3/x

    I mention BIDMAS because if I do division then multiplication working from left to right I get 3x.

    But the way you and RDKgames explained it makes me think that I've gone completely wrong. If so what is the mistake I'm making?
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    (Original post by Chrollo-Lucilfer)
    I interpreted it as 1 divided by 1/3 multiplied by x. If I multiply 1/3 and x I get. x/3 then dividing with one I get 3/x

    I mention BIDMAS because if I do division then multiplication working from left to right I get 3x.

    But the way you and RDKgames explained it makes me think that I've gone completely wrong. If so what is the mistake I'm making?
    If you had 1 \div \frac{1}{3} \times x then that would be 3x.

    But for fraction notation, you can think of the numerator and denominator as having invisible brackets around them.

    So \displaystyle \frac{1}{\frac{1}{3}x}

    actually means 1 \div \left(\frac{1}{3} \times x\right)


    Another example is e.g. 2^{3+2}

    If you were to follow BIDMAS then you might get 2^3 + 2 = 10 but there are invisible brackets so really it means

    2^{(3+2)}
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    (Original post by notnek)
    If you had 1 \div \frac{1}{3} \times x then that would be 3x.

    But for fraction notation, you can think of the numerator and denominator as having invisible brackets around them.

    So \displaystyle \frac{1}{\frac{1}{3}x}

    actually means 1 \div \left(\frac{1}{3} \times x\right)


    Another example is e.g. 2^{3+2}

    If you were to follow BIDMAS then you might get 2^3 + 2 = 10 but there are invisible brackets so really it means

    2^{(3+2)}
    Thank you. That makes a lot more sense.
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    (Original post by RDKGames)
    Just follow what Notnek did above such that x \mapsto \frac{1}{3}x

    So if \displaystyle f(x)=\frac{1}{x}

    then \displaystyle f(\frac{1}{3}x)=\frac{1}{\frac{1  }{3}x}

    then multiply top and bottom of the main fraction by 3

    P.S. It doesn't matter whether it is written as \frac{1}{3}x or \frac{x}{3} as they mean the exact same thing.
    I know x/3 and 1/3 multiplied by x is equivalent. My question is why is it written is 1/3 multiplied by x instead of x/3?
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    (Original post by Chrollo-Lucilfer)
    I know x/3 and 1/3 multiplied by x is equivalent. My question is why is it written is 1/3 multiplied by x instead of x/3?
    No reason really. Perhaps for clarity. It's not a big deal.
 
 
 
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