find the inverse f^-1 of f(x) = 3x^2, where x ≥ 0. Then find f^-1(12)

This article will help :D

https://www.khanacademy.org/math/algebra-home/alg-functions/alg-finding-inverse-functions/a/finding-inverse-functions

Hope it does help :D

To find the inverse, switch x and y in the equation, making it \(x=3y^2\) and plugging in 12, you get 2 or -2.

First, we solve f^-1, which can be done by setting f(y)=x...

Thus, we have 3y^2=x

\(y=\frac{\sqrt{3x}}{3}\).

Thus, f^-1(12) is \(y=\frac{\sqrt{3*12}}{3}=\pm2.\)