math help1

Okay I am a little bit confused about one math question can you please
Help me out?
There is two parts but I already finished part a just stuck on part b

Okay so part a. draw the reflection of f(x) = (square root X-2) in the
Line y=X

Okay I understand that but when it comes to part be I am totally

Okay here is the question!
Write the equation of the reflection in the from y=g(x)

I believe the equation is (square root x+2) +2 but x is equal too/
Than 2 and y is equal too/ greater than 0 so what do I do with this

Thanks for your help!

No, the reflection of a function across the line y=x is the inverse of the function.
You have y=f(x)=sqrt(x-2). The inverse of f(x) is not (square root x+2) +2
What we want for part b is g(x)=f^-1(x), the inverse function of x.

so that would be?????

Your original f(x)=sqrt(x-2). If you let y=sqrt(x-2) we want to find the inverse of this. There are a couple way to do this. If you square both sides you get
y^2=x-2 now add two to both sides to get
now we would interchange the variables to get
y=x^2 + 2
This should be your g(x)
You can verify that it is the inverse by composing the first function with the second to get
y=sqt((x^2 + 2) -2)=sqrt(x^2) = |x|
Since we're only concerned with x=>2 for f(x), we're only interested in x=>0 for g(x). Thus we can ignore the absolute value above and we have y=x. This is what we should get if the functions are inverses.

so what you are saying is that the equation is g(x)=x^2+2

Yes, I believe that's what I was saying (I didn't check) and that's what I think your original question was asking (I did check that.)
You should verify that f(g(x))=x and g(f(x))=y as they should for inverses.

so what you are saying is that the equation is g(x)=x^2+2

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