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Thread: Restricted domain such that inverse of a function exists.

  1. #1
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    Restricted domain such that inverse of a function exists.

    Given function g is defined by g:x --> 2x^2 -8x+11 where x < or equal to A WHERE A IS A CONSTANT

    (a)state the largest value of A which g has an inverse
    Who know how to do this question?!?!?!?!?!!?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Greensew View Post
    Given function g is defined by g:x --> 2x^2 -8x+11 where x < or equal to A WHERE A IS A CONSTANT

    (a)state the largest value of A which g has an inverse
    Who know how to do this question?!?!?!?!?!!?
    That the function has an inverse requires that there be one and only one solution $\displaystyle x$ that gives the value $\displaystyle g(y)$, and then $\displaystyle g(x)=g(y). $ As g(x) is a quadratic this is the case as long as $\displaystyle x<x_0$, where $\displaystyle (x_0,g(x_0))$ is the lowest point on the graph of $\displaystyle y=g(x).$

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    CB
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