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 \$\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