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Math Help - Function notation problem

  1. #1
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    Function notation problem

    Let the function f be defined by f(x)=5x-2a , where a is a constant. If f(10)+f(5)=55, what is the value of a?

    How do you do this?
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  2. #2
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    Er, never mind, figured it out. :P
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  3. #3
    Junior Member guildmage's Avatar
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    Note that f\left( 5 \right) = 55 - f\left( {10} \right).

    But f\left( 5 \right) = 5\left( 5 \right) - 2a = 25 - 2a

    This means that 55 - f\left( {10} \right) = 25 - 2a. Which means that f\left( {10} \right) = 30 + 2a.

    But f\left( {10} \right) = 5\left( 10 \right) - 2a = 50 - 2a.

    You can solve for a from the last two equations.

    What did you get?
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  4. #4
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    Quote Originally Posted by guildmage View Post
    Note that f\left( 5 \right) = 55 - f\left( {10} \right).

    But f\left( 5 \right) = 5\left( 5 \right) - 2a = 25 - 2a

    This means that 55 - f\left( {10} \right) = 25 - 2a. Which means that f\left( {10} \right) = 30 + 2a.

    But f\left( {10} \right) = 5\left( 10 \right) - 2a = 50 - 2a.

    You can solve for a from the last two equations.

    What did you get?
    5.
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  5. #5
    Junior Member guildmage's Avatar
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    That's correct.
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