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meriva
3 years ago
6

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

Mathematics
2 answers:
AleksAgata [21]3 years ago
4 0

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•

Nana76 [90]3 years ago
4 0
<h2>Answer:</h2>

The inverse of the function F(x) is:

          \sqrt[3]{\dfrac{19}{x}}

<h2>Step-by-step explanation:</h2>

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}}

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