Questions thread

[Hielly]

hey need help on 1(b), how do you find the domain ? of y=1-x^2, the answer says (0,2]


ty

[kyzoo]

It already gives you the domain.

domain f(x) = [-2, 2]
domain g(x) = R+ = (0, ∞)

domain (f+g) = domain (fg) = domain f(x)∩domain g(x)
= [-2, 2]∩(0, ∞)
= (0,2]

[Ilovemathsmeth]

Domain of f+g or fg is the intersection of their domains.

Domain f is [-2, 2]
Domain g is (0, infinity)

Thus the only common part for both f and g is (0, 2] and thus this is the domain for functions f+g and fg.

[Hielly]

Thanks

q.9b

[Ilovemathsmeth]

Q 9.b) For fog to be defined, the range of g must be a subset of the domain of f.

Thus, the range of g must be (-infinity, 3] or a subset of this. Draw the function g(x). This function has a range of [-1, infinity]. So, this implies that your final range of g(x) is [-1, 3] in order for fog to be defined. Find where g(x) = 3; this is for x = 2, -2. Thus your domain would most likely be [-2, 2] for domain g, which would be the same for domain fog.

Hope that helps.

[Hielly]

hey thanks for that!
another q.
say ABCD is a parrallelogram the equation of BD is y=-5x+13 and the equation of BC is y=(3x-13)/2
to find the coordinate of B i used substitution/elimination to find out the coordinate. Is it because both the equation has the relationship with B?. When i came across this question i immediately thought to use simultaneous equation, my answer to that is that there is a relationship between B. Not sure if that's a good enough answer though, need some clarification. Thanks!


Also
See attachment.
For c) i used simultaneous equations ( CD and AD) and it works. i looked at another solution that is:
because it is a rectangle
D=C-(B-A)

which are the coordinates. How did the D=C-(B-A) come about?

Thanks~

[Ilovemathsmeth]

I remember this question.

If you observe the graph, B - A = C - D; thus C - (B - A) should be equal to D, i.e. it gives approx that height. I'd still prefer simultaneous equations, they require less staring at the diagram which is often not to scale.

I should think so, it is because both lines share the coordinates associated with point B, i.e. they cross each other. Thus to solve, you would use simultaneous equations.

Hope that helps!

[Hielly]

can you still use simultaneous equation to do this? seems rather long.

The solutions just tells you to input it in the calc.

[/0]

Yes, you could find the inverse of A, or you could use Gaussian elimination (the better option): http://www.sosmath.com/matrix/system1/system1.html

But you don't need to worry about that until university

[kenhung123]

Just wondering are you doing all the questions or just questions set for homework?

[Ilovemathsmeth]

You should be able to solve it with simultaneous equations but I'd strongly advise you to just use a calculator for this question if it appears on a SAC/Exam. I was told last year that it is hardly ever asked to find the rule of a function of power 4 or solve 4 simultaneous equations. I think a few are given in Essentials just for practice.

[Hielly]

Just wondering are you doing all the questions or just questions set for homework?

All , attempting to finish the methods course this holiday.

You should be able to solve it with simultaneous equations but I'd strongly advise you to just use a calculator for this question if it appears on a SAC/Exam. I was told last year that it is hardly ever asked to find the rule of a function of power 4 or solve 4 simultaneous equations. I think a few are given in Essentials just for practice.

Alright thanks

[kenhung123]

Wowee, are you doing anything for other subjects?
What chapter you up to?

[Hielly]

Wowee, are you doing anything for other subjects?
What chapter you up to?

For now im starting methods. At the moment i have one exercise left for chapter 2. There's about 20 chapters in the essentials, so i have a long way to go!
I'll probably start Chemistry later on.. (hopefully!)

[Ilovemathsmeth]

It's perfectly possible to finish Hielly! Keep motivated - I started around 19 Dec and finished about 30 Jan. I did about 3 exercises a day as well. Good luck