Question

Which of the following is the inverse of the given function? Y=3x^5-4

Answer 1

$y\textrm{ }=\textrm{ }(\frac{x\textrm{ }+\textrm{ }4}{3} )^{\frac{1}{5} }$

Step-by-step explanation:

   Given function $y\textrm{ }=\textrm{ }3x^{5}\textrm{ }-\textrm{ }4$

   To find an inverse for any given function, which is of the form $y=f(x)$, always swap $x$ and $y$ in the equation and try to get the form  $x=f(y)$. Now, swapping back $x$ and $y$, we get the inverse function.

   On swapping $x$ and $y$, we get $x\textrm{ }=\textrm{ }3y^{5}\textrm{ }-\textrm{ }4$

$y\textrm{ }+\textrm{ }4\textrm{ }=\textrm{ }3x^{5}$

$x^{5}\textrm{ }=\textrm{ }\frac{y\textrm{ }+\textrm{ }4}{3}$

$x\textrm{ }=\textrm{ }(\frac{y\textrm{ }+\textrm{ }4}{3} )^{\frac{1}{5} }$

   Swapping back $x$ and $y$, we get $y\textrm{ }=\textrm{ }(\frac{x\textrm{ }+\textrm{ }4}{3} )^{\frac{1}{5} }$

   This is the inverse function.