Restricted domain such that inverse of a function exists.

May 2010
1
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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?!?!?!?!?!!?
 

CaptainBlack

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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 \(\displaystyle y=g(x).\)

(Draw a picture)

CB