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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- May 11th 2010, 05:56 AMGreensewRestricted 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?!?!?!?!?!!? - May 12th 2010, 05:11 AMCaptainBlack
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 $\displaystyle y=g(x).$

(Draw a picture)

CB