Respuesta :
[tex]y\textrm{ }=\textrm{ }(\frac{x\textrm{ }+\textrm{ }4}{3} )^{\frac{1}{5} }[/tex]
Step-by-step explanation:
Given function [tex]y\textrm{ }=\textrm{ }3x^{5}\textrm{ }-\textrm{ }4[/tex]
To find an inverse for any given function, which is of the form [tex]y=f(x)[/tex], always swap [tex]x[/tex] and [tex]y[/tex] in the equation and try to get the form [tex]x=f(y)[/tex]. Now, swapping back [tex]x[/tex] and [tex]y[/tex], we get the inverse function.
On swapping [tex]x[/tex] and [tex]y[/tex], we get [tex]x\textrm{ }=\textrm{ }3y^{5}\textrm{ }-\textrm{ }4[/tex]
[tex]y\textrm{ }+\textrm{ }4\textrm{ }=\textrm{ }3x^{5}[/tex]
[tex]x^{5}\textrm{ }=\textrm{ }\frac{y\textrm{ }+\textrm{ }4}{3}[/tex]
[tex]x\textrm{ }=\textrm{ }(\frac{y\textrm{ }+\textrm{ }4}{3} )^{\frac{1}{5} }[/tex]
Swapping back [tex]x[/tex] and [tex]y[/tex], we get [tex]y\textrm{ }=\textrm{ }(\frac{x\textrm{ }+\textrm{ }4}{3} )^{\frac{1}{5} }[/tex]
This is the inverse function.
