Mistake on other thread, Here is the problem:

[AznBoi]

Ok sorry about that, here is the actual problem:

g(x)=sq.rt.(2-x)

Find the inverse of g(x)

ok the answer is -x^2+2, but how come the domain is [0,infinity)??

 

[courtrigrad]

The range of $$g(x)$$ is equaled to the domain of $$g^{-1}(x)$$. The range of $$g(x)$$ is $$[0, \infty)$$. Thus the domain of $$g^{-1}(x)$$ is $$[0, \infty)$$. Or think of it like this: all the x-values of $$g^{-1}(x)$$ are really all the y-values of $$g(x)$$.

 

[AznBoi]

Oh it all makes sense now, thanks!