A Few College Level Math Questions...

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. $2^{\frac{5}{2}} - 2^{\frac{3}{2}} = 2^{\frac{3}{2}}(2 - 1)$

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

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

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 $\sqrt{2} + i$ .