Secondary Level (specifically, grade 11)
Here's a few math problems that might drive a person insane ;)
- If 2f(x) - 3f(1/x) = x^2 what is f(2)?
- What are the domain and range of the following relations?
- x^2 - 4y^2 = 25
- 4x^2 + 9y^2 = 36
- The port of Swan Harbor is 200km away from Merry Town Inlet on a bearing of N50E from Merry Town. A ship leaves Merry Town at 8am and sails N15W at 15 km/h. At the same time, a second ship leaves Swan Harbour on a course of S80W at 20km/hour. How close, to the nearest km, are the two ships at 13:00?
- Prove the identity.
1+sinx + cosx/ 1-sinx + cosx = 1+sinx / cosx
Here are a couple of hints.
I hope this helps,
If you let x = 2 then you get
2f(2) - 3f( 1/2) = 4
The difficulty is f( 1/2). So, what is f(x) when x = 1/2?
Rewrite the relation as
x 2 = 25 + 4y 2
No matter what value you choose for y, 25 + 4y 2 is non-negative so you can take its square root and find a corresponding value for x. Thus y can be any real number. However 25 + 4y 2 >= 25 so x 2 >= 25 and thus x <= -5 or x >=5.
4x2 = 36 - 9y2. Since the left side is non-negative, the right side must also be non-negative. Thus 9y 2 <= 36.
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