What is the functions restricted domain and what is its inverse function

Question

The function f(x)=(x=2)^2-1 is not one-to-one. Restrict the function's domain an find its inverse. What is the function's restricted domain and what is its inverse function?

 

I think the restricted domain:x>-2:f^-1(x)=2-2-square root x=1

Answer 1

So first thing first, is it f(x) = (x+2)²-1?  (I'll assume it is because + and = are the same button on the keyboard.

 

If so, to restrict the domain, we need to find the right side of the quadratic.  To do this, first find the vertex.  The vertex comes from the equation and it turns out to be (-2,-1).  The right side of the quadratic would be x>=-2.

 

So f^-1(x) = sqrt(x+1) - 2.  The domain of this function x>=-1 and the range is y>=-2

 

Note: the original equations restricted domain becomes the range of the inverse.

 

Hope that helps.