# F is The Function

• May 8th 2007, 06:42 AM
Rimas
F is The Function
Suppose A Function f is sich that

F(1/x)-3f(x)=x

For every x not equal to 0 find f(2)
• May 8th 2007, 06:46 AM
TD!
Substitute x = 2 and x = 1/2 and solve for f(2).
• May 8th 2007, 06:49 AM
topsquark
Quote:

Originally Posted by Rimas
Suppose A Function f is sich that

F(1/x)-3f(x)=x

For every x not equal to 0 find f(2)

Note: F(x) and f(x) are NOT the same function! Please be careful of "case" when you write these.

Quote:

Originally Posted by TD!
Substitute x = 2 and x = 1/2 and solve for f(2).

Let me expand a bit on TD's hint:

f(1/x) - 3f(x) = x

Let x = 2:
f(1/2) - 3f(2) = 2

Let x = 1/2
f(2) - 3f(1/2) = 1/2

Call f(1/2) = a and f(2) = b. Then we have the system of equations:
a - 3b = 2
-3a + b = 1/2

You want to solve this system of equations for b.

-Dan
• May 8th 2007, 04:47 PM
Rimas
• May 8th 2007, 05:32 PM
topsquark
Quote:

Originally Posted by topsquark
Note: F(x) and f(x) are NOT the same function! Please be careful of "case" when you write these.

Let me expand a bit on TD's hint:

f(1/x) - 3f(x) = x

Let x = 2:
f(1/2) - 3f(2) = 2

Let x = 1/2
f(2) - 3f(1/2) = 1/2

Call f(1/2) = a and f(2) = b. Then we have the system of equations:
a - 3b = 2
-3a + b = 1/2

You want to solve this system of equations for b.

-Dan

Solve the top equation for a:
a = 3b + 2

Insert this into the second equation:
-3[3b + 2] + b = 1/2

-9b - 6 + b = 1/2

-8b = 6 + 1/2 = 13/2

b = -13/16 = f(2)

-Dan