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
[tex]y = \sqrt[3]{ \frac{19}{x} } [/tex]
then just replace y with f^-1(x)
[tex]f(x) = \sqrt[3]{ \frac{19}{x} } [/tex]
hope this helped! have a good day ~ •lipika•
The inverse of the function F(x) is:
[tex]\sqrt[3]{\dfrac{19}{x}}[/tex]
We are given a rational function F(x) as:
[tex]F(x)=\dfrac{19}{x^3}[/tex]
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:
[tex]F(x)=y[/tex]
i.e.
[tex]\dfrac{19}{x^3}=y[/tex]
Now we interchange x and y
i.e.
[tex]\dfrac{19}{y^3}=x[/tex]
Now we solve for y as follows:
[tex]y^3=\dfrac{19}{x}\\\\i.e.\\\\y=\sqrt[3]{\dfrac{19}{x}}[/tex]
Hence, the inverse function is:
[tex]\sqrt[3]{\dfrac{19}{x}}[/tex]
