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Math Help - A Few College Level Math Questions...

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    A Few College Level Math Questions...

    I took this entry test so I could dual enroll at a college a few days ago and completely failed the college math part... Since then I've been trying to remember/learn as much as I can so I can go back and pass it... Anyway, I've been looking at sample questions similar to what I'd be going back and doing and I need help understanding the answers to a bunch of them.

    Here they are:

    2^5/2 - 2^3/2 = 2^3/2
    That is what the answer was at least. How is this possible?

    Stupid question... Are f(-x) and f^-1(x) the same thing? (inverse operation?)

    The equation x2 2√2 x + 3 = 0 has as its roots... Answer is √2 + i, √2 i.
    What is the step-by-step solution to this or any problem like it?

    If I find more questions I'll post those too. These were some of the ones I could find for now.

    Thanks for the help. It is greatly appreciated... and needed...
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  2. #2
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    Quote Originally Posted by randomperson010101 View Post
    I took this entry test so I could dual enroll at a college a few days ago and completely failed the college math part... Since then I've been trying to remember/learn as much as I can so I can go back and pass it... Anyway, I've been looking at sample questions similar to what I'd be going back and doing and I need help understanding the answers to a bunch of them.

    Here they are:

    2^5/2 - 2^3/2 = 2^3/2
    That is what the answer was at least. How is this possible?

    Stupid question... Are f(-x) and f^-1(x) the same thing? (inverse operation?)

    The equation x2 – 2√2 x + 3 = 0 has as its roots... Answer is √2 + i, √2 – i.
    What is the step-by-step solution to this or any problem like it?

    If I find more questions I'll post those too. These were some of the ones I could find for now.

    Thanks for the help. It is greatly appreciated... and needed...
    1. 2^{\frac{5}{2}} - 2^{\frac{3}{2}} = 2^{\frac{3}{2}}(2 - 1)

     = 2^{\frac{3}{2}}(1)

     = 2^{\frac{3}{2}}.


    2. No, they are not the same thing.

    f^{-1}(x) is the inverse function of f(x), while f(-x) simply means to replace each x in f(x) by -x.


    3. x^2 - 2\sqrt{2}x + 3 = 0

    x^2 - 2\sqrt{2}x + (-\sqrt{2})^2 - (-\sqrt{2})^2 + 3 = 0

    (x - \sqrt{2})^2 - 2 + 3 = 0

    (x - \sqrt{2})^2 + 1 = 0

    (x - \sqrt{2})^2 = -1

    x - \sqrt{2} = \pm \sqrt{-1}

    x - \sqrt{2} = \pm i

    x = \sqrt{2} \pm i.


    So the two roots are x = \sqrt{2} - i and \sqrt{2} + i.
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