show that the function f(x)=3(x-5)^2 + 7 is not one to one?

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  • 3 weeks ago

    f(4) = 10

    f(6) = 10

    f(4) = f(6)

    That is enough to show that the function isn't one to one.

  • 3 weeks ago

    That's the function for a parabola with a vertex at (5, 7).

    It's not one-to-one because there are points in the domain that correspond to the same value in the range. In other words, it would fail the horizontal line test. Specifically for any point to the left of 5, there is a corresponding value the same distance to the right of 5 that results in the same y-value.

    We can show that by computing f(3) and f(7), for example:

    f(3) = 3(3 - 5)² + 7

    = 3(-2)² + 7

    = 3*4 + 7

    = 12 + 7

    = 19

    f(7) = 3(7 - 5)² + 7

    = 3(2)² + 7

    = 3*4 + 7

    = 12 + 7

    = 19

    That's just one example, but that's all you need to show that the function is *not* one-to-one.

  • Except that it is.  It's a quadratic function, and quadratic functions are one-to-one

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