Please explain each step thank you
Solved: y^2-8x +7
(y-4)^2 -9
sqrt(x-9)+4 = y
+118608 g(x) is a concave up parabola
\(g(x)=x^2-8x+7\\ g(x)=(x-7)(x-1)\\ \text{roots are at x= 7 and x= 1}\\ \text{Axis of symmetry = 4} \)
x=4 g(4)= -3*3 = -9
So the vertex is (4,-9)
Since the domain is \((4,\infty)\) the range is \((-9,\infty) \)
So the domain and range of the inverse must be the other way around.
For \(g^{-1}(x)\)
The domain is \((-9,\infty) \) abd the range is \((4,\infty)\)
Here is the graph.
https://www.desmos.com/calculator/lgob2ihohq
This maths underneath is not needed to answer the question but I have done it so I might as well leave it.
\(Let\;\;y=g(x)\\ y=x^2-8x+7 \qquad x>4\\ y-7=x^2-8x\\ y-7+16=x^2-8x+16\\ y+9=(x-4)^2\\ \pm\sqrt{y+9}=x-4\\ \text{But x-4 is positive, so}\\ x-4=\sqrt{y+9}\\ x=\sqrt{y+9}+4\\ g^{-1}(x)=\sqrt{x+9}+4\)
