you multiply it by the root of three and then square everything, not three.i feel pretty good about my calculus III final. only i know i got one question slightly wrong. to integrate a function we had to find an inverse function, i KNOW that i got it wrong but i still cant understand WHY i got it wrong.

the function was the square root of x/3. i had the inverse function as 9x^2. the right answer is 3x^2 but i cant understand why. in the original function, you take x, divide it by three and take the root of EVERYTHING. its inverse should: take x, multiply it by 3 THEN square everything. 9x^2. but i can compute some examples and show that 3x^2 IS the right inverse, but cant figure out where my reasoning is wrong.