Question

The function f(x) = (x + 1)^2 can be inverted to find its inverse by restricting the domain to what?

Answer 1

`\begin{gathered} f(x)=(x+1)^2 \\ \\ \text{Vertex form of a quadratic equation:} \\ f(x)=a(x-h)^2+k \end{gathered}`

In the given function the vertex (h,k) is (-1,0).

To find the inverse of the given function as it is not a one to one function (has the same value f(x) for more that one value of x) you restrict the domain to get a function one to one.

In a quadratic function as given use the vertex to restric the domain; restric the domain using coordinate x of the vertex.

In the given equation the coordinate x of the vertex is -1, then you can restirc the domain as follow:

`\begin{gathered} x\ge-1 \\ x\le-1 \end{gathered}`