# Restricted domain such that inverse of a function exists.

#### Greensew

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

MHF Hall of Fame
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