I'm having difficulty understanding this transformation.
What is the correct order of these transformations? How do I find this correctly.
I understand that $y=f^{-1}(x)$ can refer to switching the coordinates (the inverse) (appears as a reflection in the line $y=x$)
I also understand that replacing $x$ with $x+2$ results in points that appear two units left of their original locations.
I am not sure if I can first take the input $x$ and move the point two units to the left to obtain $(8,8)$ which would follow $y=f(x+2)$ then take the inverse of that point. So the point would be $(8,8)$ which doesn't seem correct.
It seems the correct way is the take the inverse first, $y=f^{-1}(x)$ So reflect in the line $y=x$ to obtain the point $(8,10)$ then use the input (x+2) which results in the point $(6,10)$ Can someone please walk me through this?
The answer says it should be $(6,10)$ It seems that we take the inverse first then replace $x$ with $x+2$ Can someone explain?
To un-nest this composition of functions...
$f(10) = 8\\ f^{-1}(8) = 10\\ f^{-1}(6+2) = 10$
$(6,10)$ is the corresponding point.
or more abstractly
$y = f^{-1}(x+2)\\ f(y) = x+2\\ x = f(y) - 2$