$f(x)=4+\sqrt{x-2}\\f^{-1}(x)=x^2-8x+18\\g(x)=x$
Obtain the graph of $f$ , $f^{-1}(x)$, and $g(x)=x$ in the same system of axes.
About what pair (a, a) are (11, 7) and (7, 11) reflected about?
After I graphed three equations, there is no pair point met at (11,7) and (7,11).
What does this question mean?
About what pair (a, a) are (11, 7) and (7, 11) reflected about?
Your inverse of $f$ is correct, so graphing all three functions should yield the following:
Where by setting all three functions equal to each other and solving for $x$ we get the intersection of the functions at the point $(6,6)$ (a point of the form $(a,a)$ (where $a$ is a real number)). However, this is not the pair on the line $g(x) = x$ where $(11,7)$ and $(7,11)$ are reflected about. Points of the form $(a,b), (b,a)$ (where $b$ is a real number) are reflected about the midpoint between the two points.
So, in this case the midpoint between $(11,7)$ and $(7,11)$ is $(9,9)$, i.e. the point of reflection shown in the (piece of the) graph below. Keep in mind: $f(11) = 7$ and $f^{-1}(7) = 11$