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  1. #1
    Senior Member DivideBy0's Avatar
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    function

    f)
    If g:[1,a] -> R where g(x) = f(x) and g is one-one, write down the largest possible
    value of a.

    This is part f) of the Q.2, which gives the function $\displaystyle -2x^2+5x-3$ for $\displaystyle x \in [1,\infty)$
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  2. #2
    Senior Member DivideBy0's Avatar
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    Does anyone else think $\displaystyle a$ should be the maximum of $\displaystyle f(x)$?
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by DivideBy0 View Post
    f)
    If g:[1,a] -> R where g(x) = f(x) and g is one-one, write down the largest possible
    value of a.

    This is part f) of the Q.2, which gives the function $\displaystyle -2x^2+5x-3$ for $\displaystyle x \in [1,\infty)$
    I'm just a little confused over all of this. Pretend that I haven't done the problem up to this point. What the heck is f(x) anyway? Are you saying $\displaystyle f(x) = -2x^2 + 5x - 3$?

    You have $\displaystyle g: [1, a] \to \mathbb{R}: g(x) = f(x)$. You know that g is one-to-one.

    So the question is really: Given the restriction of the domain of f to [1, a], what is the largest value of a such that f(x) is one-to-one.

    If your $\displaystyle f(x) = -2x^2 + 5x - 3$ then it looks like x = 1 is on the left of the vertex, so a would have to be the x coordinate of the vertex of f(x). (That's the accurate way to say what I think you were trying to say.)

    -Dan
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    Quote Originally Posted by DivideBy0 View Post
    Does anyone else think $\displaystyle a$ should be the maximum of $\displaystyle f(x)$?
    Yes that is the correct answer.
    An easy to see it is to simlpy graph the function.
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  5. #5
    Senior Member DivideBy0's Avatar
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    Quote Originally Posted by topsquark View Post
    I'm just a little confused over all of this. Pretend that I haven't done the problem up to this point. What the heck is f(x) anyway? Are you saying $\displaystyle f(x) = -2x^2 + 5x - 3$?
    Thanks both of you
    I too was a bit confused over its ambiguity. It didn't say that $\displaystyle -2x^2+5x-3$ was f(x), so I guess it had to be assumed.
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