Question

Could someone explain the difference between the domain of f(x) = sqrt(2x^3 - 9x^2) vs 1/(sqrt(2x^3 - 9x^2))

I used this website to try and help but I still don't understand why 9/2 is not included in the domain of the second function.

https://www.symbolab.com/solver/function-domain-calculator/domain%20f%5Cleft%28x%5Cright%29%3D%5Cfrac%7B1%7D%7Bsqrt%5Cleft%282x%5E%7B3%5E%7B%20%7D%7D-%209x%5E%7B2%7D%5Cright%29%7D/?origin=button

Answer 1

Never mind. That website is wrong. Wolfram Alpha got it right. 0 cannot be in the denominator so the domain of the second function is (9/2), infinite)

Answer 2

I assume the 2nd should have a square root in it , like this:
\[ \frac{1}{\sqrt{2x^3 -9x^2} }\]
?

if so the rules are:
no divide by 0
not square root of a negative number