Respuesta :

altavistard

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:

The inverse function of [tex]f(x) =\frac{19}{x^3}[/tex]

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

Step-by-step explanation:

[tex]f(x) = \frac{19}{x^3}[/tex]

Steps to inverse the functions:

Step 1: x ⇔ y

[tex]x=\frac{19}{y^3}[/tex]

Step 2 : now solve the equation for y:

[tex]y^3=\frac{19}{x}[/tex]

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

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

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

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