Hello, I'm back again. Thanks for the help with the last problems! You guys have definitely been a huge help to me thus far, but I still have some more problems and well little time left before school. So, if you could again lend me a hand that would be great. Some of the questions I have been able to get through okay, but I'm unsure of the answer, while others are complete a total calculator problems that I'm having major difficulty with. I'm not calculator savvy at all (and I just checked I have a TI-84 not 83), so those problems on the packet I've been having major trouble with.
So if you could help me with three more problems that would be great!
1) Let \(\displaystyle \ f(x) \ = \sqrt {x-3}\) and \(\displaystyle \ g(x) \ = \ x^{2}+1\). Compute \(\displaystyle (g \ o \ f)(x)\), state its domain in interval notation.
Here is what I have so far:
\(\displaystyle (( \sqrt {x-3}^{2}+1)( \sqrt{x-3})\)
\(\displaystyle ((x-3)+1)( \sqrt {x-3})\)
\(\displaystyle (x-2)( \sqrt {x-3})\)
The domain, I have little trouble with it is the interval notation I'm not understanding. If someone could explain it to me or lead me in the right direction that would be great.
2) Find the points of intersection of:
\(\displaystyle x^{2} + y^{2} = 4\) which I get to \(\displaystyle \frac {x^{2}}{4} + \frac {y^{2}}{4}\) which I believe is the equation of a circle (have yet to graph).
&
\(\displaystyle x^{2} + y^{2} - 4x - 4y = -4\), for this one I think you do \(\displaystyle x^{2} + y^{2} - 4(x+y) = -4\), but it doesn't look right at all because from there I would divide the -4 on both sides to equal it to 1.
So, could you help me boil down the second equation to the proper equation that I can graph to find the intersections.
And lastly,
3) Given that \(\displaystyle f(x) = \frac{2x^{2}}{5x^{2}-9x-2}\) Find lim ( underneath it is a x-->? ) f(x). Also state the domain of their function.
This one I have absolutely no idea how to begin, so if you could please help me with the first step that would be great.
Thanks yet again!
-Cheyenne
So if you could help me with three more problems that would be great!
1) Let \(\displaystyle \ f(x) \ = \sqrt {x-3}\) and \(\displaystyle \ g(x) \ = \ x^{2}+1\). Compute \(\displaystyle (g \ o \ f)(x)\), state its domain in interval notation.
Here is what I have so far:
\(\displaystyle (( \sqrt {x-3}^{2}+1)( \sqrt{x-3})\)
\(\displaystyle ((x-3)+1)( \sqrt {x-3})\)
\(\displaystyle (x-2)( \sqrt {x-3})\)
The domain, I have little trouble with it is the interval notation I'm not understanding. If someone could explain it to me or lead me in the right direction that would be great.
2) Find the points of intersection of:
\(\displaystyle x^{2} + y^{2} = 4\) which I get to \(\displaystyle \frac {x^{2}}{4} + \frac {y^{2}}{4}\) which I believe is the equation of a circle (have yet to graph).
&
\(\displaystyle x^{2} + y^{2} - 4x - 4y = -4\), for this one I think you do \(\displaystyle x^{2} + y^{2} - 4(x+y) = -4\), but it doesn't look right at all because from there I would divide the -4 on both sides to equal it to 1.
So, could you help me boil down the second equation to the proper equation that I can graph to find the intersections.
And lastly,
3) Given that \(\displaystyle f(x) = \frac{2x^{2}}{5x^{2}-9x-2}\) Find lim ( underneath it is a x-->? ) f(x). Also state the domain of their function.
This one I have absolutely no idea how to begin, so if you could please help me with the first step that would be great.
Thanks yet again!
-Cheyenne