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Math Help - F is The Function

  1. #1
    Member Rimas's Avatar
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    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)
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  2. #2
    TD!
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    Substitute x = 2 and x = 1/2 and solve for f(2).
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Rimas View Post
    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! View Post
    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
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  4. #4
    Member Rimas's Avatar
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    So the answer is b=3.5a?
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  5. #5
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by topsquark View Post
    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
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