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Math Help - Simple Exponential Equation

  1. #1
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    Simple Exponential Equation

    f(x) = 2 + 3x

    What is f(2x) - f(x)?
    --------------------

    It's embarrassing to ask about this question, but I can't remember how to solve it for the life of me.

    Thanks in advance.
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  2. #2
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    Re: Simple Exponential Equation

    What have you done ?
    First : f(2x)= ?
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  3. #3
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    Re: Simple Exponential Equation

    I'm assuming that f(2x) = 2(2+3x)?
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  4. #4
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    Re: Simple Exponential Equation

    No. f(x) is a notation that says "the function operated on the value x". Here we are told \displaystyle \begin{align*} f(x) = 2 + 3^x \end{align*}, which says that whatever value you put in, is what you will raise 3 to the power of, and then add 2 to. So if instead we put in 2x we get f(2x). If the same function operates on 2x (so this is what we raise 3 to the power of and then add 2 to), what will we get?
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    Re: Simple Exponential Equation

    Quote Originally Posted by Fratricide View Post
    I'm assuming that f(2x) = 2(2+3x)?
    No, you are confusing 2f(x) with f(2x).
    f(x) = 2+3x
    It is true for any symbol, for example :
    f(v) = 2+3v
    or, for example :
    f(t) = 2+3t
    Your difficulty is to understand that t=2x in the case of f(2x)
    Then, f(2x)= ?
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    Re: Simple Exponential Equation

    Ah, thank you. Such a noob mistake.

    Answer: 3x(3x​-1)?
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  7. #7
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    Re: Simple Exponential Equation

    No
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    Re: Simple Exponential Equation

    Quote Originally Posted by Fratricide View Post
    Ah, thank you. Such a noob mistake.
    Answer: 3x(3x​-1)?
    Yes
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    Re: Simple Exponential Equation

    Tie breaker: " 3^x(3^x- 1)" is the correct answer to the original question "what is f(2x)- f(x)". It is NOT the correct answer to the last question "what is f(2x)".
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  10. #10
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    Re: Simple Exponential Equation

    OK. This is what I meant.
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  11. #11
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    Re: Simple Exponential Equation

    Quote Originally Posted by HallsofIvy View Post
    Tie breaker: " 3^x(3^x- 1)" is the correct answer to the original question "what is f(2x)- f(x)". It is NOT the correct answer to the last question "what is f(2x)".
    or " (3^x)^2 -3^x"
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  12. #12
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    Re: Simple Exponential Equation

    Quote Originally Posted by votan View Post
    or " (3^x)^2 -3^x"
    Use this identity to prove the 1 = 2. No kidding. It's real.
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