question is
the graph $\displaystyle y=(x-2)^{2}-1$ represents y=f(x). What are the coordinates of the points that would be invariant for the transformations?
then it has a list of 5 equations to find these points for.
question is
the graph $\displaystyle y=(x-2)^{2}-1$ represents y=f(x). What are the coordinates of the points that would be invariant for the transformations?
then it has a list of 5 equations to find these points for.
I think you're a little on the wrong track here. A fixed point is one that doesn't change after a transformation. Consider this simple example f(x)=x and the transformation f --> f^2. What points are fixed? In other words what values of x satisfy f(x)=f^2(x). The solution is fairly simple:
$\displaystyle f(x)=f^2(x)$
$\displaystyle x=x^2$
x=0 or x=1.
Now let's look at your problem:
The transformation is f --> -f, so:
$\displaystyle f(x)=-f(x)$
$\displaystyle 2f(x)=0$
$\displaystyle f(x)=0$
$\displaystyle (x-2)^2-1=0$
Solve that and you'll have your answer.