The inverse of this function would be [tex] f(x) = \sqrt[3]{\frac{19}{x}} [/tex]
In order to find any inverse function, you must start by switching the x and f(x). After you've done that, you must solve for the new f(x). The result will be your inverse function. The work for this one is below.
f(x) = [tex] \frac{19}{x^{3}} [/tex] ----> Switch the x and f(x)
x = [tex] \frac{19}{f(x)^{3}} [/tex] ----> Cross multiply.
[tex] f(x)^{3} [/tex] = [tex] \frac{19}{x} [/tex] ----> Take the cube root of both sides
f(x) = [tex] \sqrt[3]{\frac{19}{x}} [/tex]
