Here's a few math problems that might drive a person insane ;)

1. If 2f(x) - 3f(1/x) = x^2 what is f(2)?
   
   
2. What are the domain and range of the following relations?
   • x^2 - 4y^2 = 25
   • 4x^2 + 9y^2 = 36
   
   
3. 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?
   
   
4. Prove the identity. 1+sinx + cosx/ 1-sinx + cosx = 1+sinx / cosx

Here are a couple of hints.

1. 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?
   
   
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.