Answer:
[tex]{f}^{ - 1} (x) = \sqrt[3]{ \frac{19}{x} } [/tex]
Step-by-step explanation:
To find the inverse of
[tex]f(x) = \frac{19}{ {x}^{3} } [/tex]
We let
[tex]y = \frac{19}{ {x}^{3} } [/tex]
Interchange x and y
[tex]x = \frac{19}{ {y}^{3} } [/tex]
Solve for y,
[tex]x {y}^{3} = 19[/tex]
[tex] {y}^{3} = \frac{19}{x} [/tex]
Take cube root of both sides
[tex]y = \sqrt[3]{ \frac{19}{x} } [/tex]
Therefore
[tex] {f}^{ - 1} (x) = \sqrt[3]{ \frac{19}{x} } [/tex]
