C3 - Maths Functions Help

I heard a different way to find the range of a function is to interchange the x and y and then find the domain instead. Then substitute the domain back into the original function and find what values work. I just wrote a really rough note a few months ago. I have no idea if it works or not. If anyone knows and can explain it better, any help would be appreciated.
Thanks

Give us an example, and i'll help you.

f(x) = 1 - x^2
y = 1 - x^2
interchange y and x
x = 1 - y^2
rearrange
y = sqrt 1- x
therefore the domain is x greater than or equal to zero, since you cannot sqrt a negative.
Now rearrange and substitute back into original.
y = 1 - x^2
so if the x values have to be equal or greater than zero....the largest y value is 1.

IS THIS A VALID METHOD !
What if its a new method :O ? I doubt it but lmao that would be awesome

Oh and will it work with all functions?

I heard a different way to find the range of a function is to interchange the x and y and then find the domain instead. Then substitute the domain back into the original function and find what values work. I just wrote a really rough note a few months ago. I have no idea if it works or not. If anyone knows and can explain it better, any help would be appreciated.
Thanks

It's the same as saying that the domain of a function is the same as the range of its inverse function (what you've calculated) and the range of the function is the same as the domain of the inverse function.

Right, and is that true for any function? That its domain is equivalent to the range of the inverse function and the range is equivalent to the domain of the inverse function?