# Thread: How would I solve the domain of the inverse for f(x) (given f(x)'s domain).

1. ## How would I solve the domain of the inverse for f(x) (given f(x)'s domain).

I have the equation f(x) = , and its domain is .

I solved for its inverse, .

The domain for f-1(x) is originally x is less than or equal to 3, but with f(x)'s given domain, how do I solve for the new domain of f-1(x)?

Can someone guide me through the steps needed to solve such a problem?

2. ## Re: How would I solve the domain of the inverse for f(x) (given f(x)'s domain).

The domain of $\displaystyle f^{-1}$ is the range of f. (Going from f to $\displaystyle f^{-1}$ swaps "domain" and "range".) f(0)= 6 and as x goes to infinity, f(x) goes to negative infinity. So the domain of $\displaystyle f^{-1}$ is all number less than or equal to 6.

(The inverse function to $\displaystyle -x^2+ 6]$ is $\displaystyle \sqrt{-x+ 6}$, not $\displaystyle \sqrt{-x+ 3}$. Was that a typo?)

3. ## Re: How would I solve the domain of the inverse for f(x) (given f(x)'s domain).

Thank you so much! And yes, that was a typo, sorry!