
Erin
Secondary Level (specifically, grade 11)
Student
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/ 1sinx + cosx = 1+sinx / cosx
Hi Erin,
Here are a couple of hints.

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 nonnegative 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.

4x^{2} = 36  9y^{2}. Since the left side is nonnegative, the right side must also be nonnegative. Thus 9y^{ 2} <= 36.
I hope this helps,
Penny
Go to Math Central

