Question

Which is the inverse of the function F(x)=19/x^3

Answer 1

`{f}^( - 1) (x) = \sqrt[3]{ (19)/(x) }`

Explanation:

To find the inverse of

`f(x) = \frac{19}{ {x}^(3) }`

We let

`y = \frac{19}{ {x}^(3) }`

Interchange x and y

`x = \frac{19}{ {y}^(3) }`

Solve for y,

`x {y}^(3) = 19`

`{y}^(3) = (19)/(x)`

Take cube root of both sides

`y = \sqrt[3]{ (19)/(x) }`

Therefore

`{f}^( - 1) (x) = \sqrt[3]{ (19)/(x) }`