Restricted domain such that inverse of a function exists.

• May 11th 2010, 05:56 AM
Greensew
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?!?!?!?!?!!?
• May 12th 2010, 05:11 AM
CaptainBlack
Quote:

Originally Posted by 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?!?!?!?!?!!?

That the function has an inverse requires that there be one and only one solution $x$ that gives the value $g(y)$, and then $g(x)=g(y).$ As g(x) is a quadratic this is the case as long as $x, where $(x_0,g(x_0))$ is the lowest point on the graph of $y=g(x).$

(Draw a picture)

CB