More function help! D= (1 Viewer)

[starryblue]

I'm stuck on these questions! D= can anyone please help?
1) What values of x would it be posibel to sketch the curve y= root of (x-6)(3-x)(x+4)?
2) find the values of a for which F((2a-3)/15)=a^2, i got to the answer 2a^3-3a^2-8a+3=0 but i dunno how to factorise and i might be wrong.
3) the polynomial P(x)=x^5+ax^3+bx leaves a remainder of 5 when divided by (x-2), where a and b are numerical constants, find the remainder when P(x) is divided by (x+2).
4) if 0<x<1 and y is positive integer, find the largest value in the set {x/y, y/x, X^y, y-x, xy} and explain why.
5)sketch a periodic function y=f(x)={1, -1<x<0); 3-2x^3, 0<=x<=1} with a period of 2 in the domain -3<=x<=3. can you please explain how you do it?
6) find the greatest and smallest values of cos^2x.
7) find the greatest and smallest values of 2-cos^2x.
8) let g(x)=sinx and h(x)=x^2-7x
i) determine h.g(x)
ii) solve h.g(x)=0 for 0 degrees<=x<=360 degrees.

thanks a lot for the help =)

 

[Alkanes]

Question 1 : Umm to find the values of x you would need to let y = 0. SBS square both side leaves (x-6)(3-x)(x+4) = 0 values of x are 6, 3 and -4. As for the function not sure what it's called
Question 2: Use polynomials or try and factorise it by completing the square some how.
Question 3: Solve simultaneous by first subbing in P(2) for the values of x into the equation = 5, and P(-2) then solve simultaneously to get the values for a and b then just sub it back in again to find remainder
Question 4: Huh?
Question 5: Think it's a piece meal function its asking for? It should of also have given u the condition
Question 6: I think its +- 1. :S
Question 7: Greatest value is 2 smallest value is -2
Question 8: a) Just expand it.
=
b)Solve using ASTC.

Hmm edit: For question 2 check your algebra, it looks kinda wrong. Should be Then factorise it or use the quadratic formula