How would you solve this?

Question

Find the inverse of f(x)=|x-3|. State whether or not the inverse is a function. If it is not, what do we need to do to make it a function.

Answer 1

Abs(m)=sqrt(m^2)

So the function can be written

Y = sqrt((x-3)^2)

Inverse goes like this:

X= sqrt((y-3)^2) <-- swaps

X^2 = (y-3)^2

Sqrt(x^2) = y-3

Abs(x)=y-3

Abs(x)+3=y

Technically the inverse is

Y= 3 +or- abs(x)

So no it is not a function unless the domain

Is restricted to either positive or negative