find domain of inverse

Question

g(x)= x² − 6x + 7 for x >4. By first completing the square, find and expression for g^-1 (x) and state the domain of g^-1

^{I found the inverse to be √(x+2) + 3}

^{is the domain x≥-2?}

Answer 1

The answer that you have is correct.

You would complete the square using +9

g(x)= (x-3)² +7-9 This is done to keep it balanced

g(x)= (x-3)² +2

Switch the G(x) to y and reserve that x and y

x= (y-3)²+2 Now solve for y

y= Squrt (x+2) +3

The domain is limited by the square rt. It can't be <0 So the domain is x< and = to -2.

You did a great job