inverses

Hey can you put the parenthesis in the right spots?

Your notation is fine Jenny,     (although brackets do cut down any possibility of confusion) 

f(x)=3/5x^3-9

$f(x)=\frac{3}{5}x^3-9\\ let \;\;y=f(x)\\ y=\frac{3}{5}x^3-9\\ \text{make x the subject}\\ 5y=3x^3-45\\ \frac{5y+45}{3}=x^3\\ x=\sqrt[3]{\frac{5y+45}{3}}\\ so\\ f^{-1}(x)=\sqrt[3]{\frac{5x+45}{3}}\\$

I don't know what they want for the verification ....

Here is graph validation I guess

A function and its inverse are reflections of one another over the line y=x

Latex

f(x)=\frac{3}{5}x^3-9\\
let \;\;y=f(x)\\
y=\frac{3}{5}x^3-9\\
\text{make x the subject}\\
5y=3x^3-45\\
\frac{5y+45}{3}=x^3\\
x=\sqrt[3]{\frac{5y+45}{3}}\\
so\\
f^{-1}(x)=\sqrt[3]{\frac{5x+45}{3}}\\