Given f(x)=(x-6)^2+7 find f^-1(x) then state whether f^-1(x) is a function

For this case we must find the inverse of the following function:

For this we follow the steps below:

Replace f (x) with y:

We exchange the variables:

We solve the equation for "y", that is, we clear "y":

We subtract 7 on both sides of the equation:

We apply square root on both sides of the equation to eliminate the exponent:

We add 6 to both sides of the equation:

We change y by

Answer;

If it is a inverse function.