Alright, I have a really big exam tomorrow in Pre-Calculus and I need to make sure I get an A on it. So I've been studying my review sheet for hours on end, but without a teacher here I can't tell if it's right or not. So could someone check these and see if they're right?

1. Find (fg)(x) for f(x)= 1/x and g(x)=x²

(fg)(x)=x

2. Find all real zeros for f(x)= -6x⁴+150x²

x= 0, x= 5, x= -5

3. For Triangle ABC, cos B= -0.5, if so then angle B is approximately how many degrees?

120^o or 240^o (-240^o ?)

4. Use the rational root theorem to determine all the possible rational zeros for the polynomial equation f(x)= x⁴-2x³-4x²+2x+3

(+/-)3, (+/-) 1

5. Which of the following secant functions has a phase shift of -3{pi}/2 and a period of 8{pi}/7 ?

a.) y= sec [(7x/4) + (21{pi}/8)]
b.) y= sec [(7x/4) - (21{pi}/8)]

1. Should be 1/x² I believe. So it's f(x^2), then given that f(x)=1/x, it's the answer that I gave. http://www.purplemath.com/modules/fcncomp3.htm

2. You got 2 right.

3. It would be 120. Think about it, if cosb=-.5 then do arccos to both sides and you get 120 degrees.

4. Sorry, never learned the rational root theorem. Just plug it into a graphing calculator and find the zeros to check your work.

5. Unfortunately I don't remember which part of the function is a phase shift and which is the period well enough to tell you either way.

I don't know how much of pre-calc you do (or the school I am tutoring for doesn't do) but I made this for someone I tutored in pre-calc today so it may be helpful to you:
https://docs.google.com/open?id=0BzfblCPuj7O9MmI0NjQ2MDgtMTNlYy00M2MyLTg4NjUtY2RiZTRmMDRjNDVj

You can ignore the last bit about limits, that was just for me.


Good luck, Calculus is much easier than pre-calc for most people so there is a light at the end of the metaphorical tunnel.

First, I highly recommend this website: http://www.physicsforums.com/.

I know its says "physics," but just go to Homework & Coursework Questions => Precalculus Mathematics, and, as long as you make sure to read the basics of the forum rules, you should get a good help in a few hours.

Anyway, let's see what I know!

1.

(f g) (x) = f(x) g(x), assuming (f g) means multiplication between the two functions f and g. So, this is true if and only if f(x) g(x) = (1/x)(x²) = x² / x = x / 1 = x. Thus, indeed, you are correct.

2.

-6x⁴ + 150x² = 6x² (-x² + 25). (Note: the zeros of a function are what is often called solutions of a function, i.e. values that make the equation equal to zero when substituted for the variable (in this case, x).) Clearly, 6x² = 0 when x = 0, and -x² + 25 = 0 if and only if x = +-sqrt{25} = +-5, i.e. plus or minus 5. Therefore, you are again correct.

3.

Well, if you can use a calculator, its obviously Arccos(-0.5) = cos^-1(-0.5) (different ways of saying it, same thing), which gives +120. However, it seems you are supposed to use a method which approximates the angle (so, not using a calculator), which I have no knowledge of.

4.

I don't really remember this one, but I do know, as another method, you could guess zeros (let this be k) and just long divide (x - k) into the given equation, which should give you a cubic equation, repeat, get a squared one, and then you should be able to solve it...

5.

I don't remember this, either, but http://en.wikipedia.org/wiki/Sine_wave should suffice.

Ah I didn't even stop to consider that it was multiplication. If this is the case the above quote is correct. My post assumed that you lacked the unicode character for a composite function and instead were denoting it as "fg", if it is a composite refer to my answer, if not refer to 5hassay's.

Yea, I agree with this. I remember finding pre-calculus pretty difficult, as a lot of things seemed ambiguous, things were not always clear, and there was just a lot of information thrown at you without giving it much meaning or concept. Yet, I didn't have the greatest teacher, and the textbook was worse than generic garbage, in my opinion.

I found that calculus was basically the opposite of everything above, that is for high school (i.e. secondary school). On that note, I recommend the textbook "Calculus, A First Course," by (essentially) James Stewart, that is, if you're taking calculus for the first time.

I found calculus to be easier mainly because for some things they gave you a shortcut for doing things instead of the stupid long way (i.e., derivatives). I *hate* calculating derivatives with limits.

....Screw this I'm going back to school.

Hahaha, then you would really hate proving limits

I got As all through high school, but I haven't used it in years, so I can't help, unfortunately. Had to say: it's awesome that these forums have people who are willing and able to help with this stuff. Yay Math and Science!

Thank you all for helping out. Hopefully I did well enough on the exam to pull my grade up a bit. I thought I had an 89/B before the exam, but it turns out I bombed a test and it dropped me down to an 80/B. Maybe this will bring it up to an A.

I don't know how she expects us to do well on her tests when they're only 10 questions. It's like she purposely sets you up to fail.

my thought exactly people here are lovely

I used to know this stuff a few years ago.

Now it's gibberish.

Proving anything is a pain.