Question

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

Answer 1

set f(x) equal to y

y = 19/ x^3

swap x and y

x = 19/y^3

make y the subject

xy^3 = 19

y^3 = 19/x

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

then just replace y with f^-1(x)

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

hope this helped! have a good day ~ •lipika•

Answer 2

Answer:

The inverse of the function F(x) is:

          $\sqrt[3]{\dfrac{19}{x}}$

Step-by-step explanation:

We are given a rational function F(x) as:

$F(x)=\dfrac{19}{x^3}$

The steps to find the inverse function of a given function f(x) are as follows:

1.   Put f(x)=y

2.  Interchange the value of x and y

3.  Solve for y.

Hence, we find the inverse of F(x) as follows:

$F(x)=y$

i.e.

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

Now we interchange x and y

i.e.

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

Now we solve for y as follows:

$y^3=\dfrac{19}{x}\\\\i.e.\\\\y=\sqrt[3]{\dfrac{19}{x}}$

      Hence, the inverse function is:

                 $\sqrt[3]{\dfrac{19}{x}}$