Question

What is the inverse function of f(x) = 19/x^3

Answer 1

Answer:

Step-by-step explanation:

1)  Replace f(x) with y:   y = 19/x^3

2) Interchange x and y:  x = 19/y^3

3) Solve this result for y:  xy^3 = 19, or y^3 = 19/x, or

   

    y = ∛[19/x]

                                                         -1

4.  Replace this y with the label    f    (x) =  ∛[19/x]

Answer 2

Answer:

The inverse function of $f(x) =\frac{19}{x^3}$

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

Step-by-step explanation:

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

Steps to inverse the functions:

Step 1: x ⇔ y

$x=\frac{19}{y^3}$

Step 2 : now solve the equation for y:

$y^3=\frac{19}{x}$

$y=\sqrt[3]{\frac{19}{x}}$

The above equation is the inverse of the given function f(x).

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