# A Few College Level Math Questions...

• Mar 28th 2010, 06:28 PM
randomperson010101
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...
• Mar 28th 2010, 06:35 PM
Prove It
Quote:

Originally Posted by randomperson010101
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. $\displaystyle 2^{\frac{5}{2}} - 2^{\frac{3}{2}} = 2^{\frac{3}{2}}(2 - 1)$

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

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

2. No, they are not the same thing.

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

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

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

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

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

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

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

$\displaystyle x - \sqrt{2} = \pm i$

$\displaystyle x = \sqrt{2} \pm i$.

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